Tracy–Widom distribution (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Tracy–Widom distribution" in English language version.

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Baik, Deift & Johansson (1999). Baik, J.; Deift, P.; Johansson, K. (1999), "On the distribution of the length of the longest increasing subsequence of random permutations", Journal of the American Mathematical Society, 12 (4): 1119–1178, arXiv:math/9810105, doi:10.1090/S0894-0347-99-00307-0, JSTOR 2646100, MR 1682248.
Majumdar & Nechaev (2005). Majumdar, Satya N.; Nechaev, Sergei (2005), "Exact asymptotic results for the Bernoulli matching model of sequence alignment", Physical Review E, 72 (2): 020901, 4, arXiv:q-bio/0410012, Bibcode:2005PhRvE..72b0901M, doi:10.1103/PhysRevE.72.020901, MR 2177365, PMID 16196539, S2CID 11390762.
Johnstone (2007, 2008, 2009). Johnstone, I. M. (2007), "High dimensional statistical inference and random matrices" (PDF), International Congress of Mathematicians (Madrid, 2006), vol. 1, European Mathematical Society, pp. 307–333, arXiv:math/0611589, doi:10.4171/022-1/13, ISBN 978-3-98547-036-5, MR 2334195, S2CID 88524958. Johnstone, I. M. (2008), "Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy–Widom limits and rates of convergence", Annals of Statistics, 36 (6): 2638–2716, arXiv:0803.3408, doi:10.1214/08-AOS605, PMC 2821031, PMID 20157626. Johnstone, I. M. (2009), "Approximate null distribution of the largest root in multivariate analysis", Annals of Applied Statistics, 3 (4): 1616–1633, arXiv:1009.5854, doi:10.1214/08-AOAS220, PMC 2880335, PMID 20526465.
Tracy & Widom (1996). Tracy, C. A.; Widom, H. (1996), "On orthogonal and symplectic matrix ensembles", Communications in Mathematical Physics, 177 (3): 727–754, arXiv:solv-int/9509007, Bibcode:1996CMaPh.177..727T, doi:10.1007/BF02099545, MR 1385083, S2CID 17398688
Baik, Deift & Johansson 1999 Baik, J.; Deift, P.; Johansson, K. (1999), "On the distribution of the length of the longest increasing subsequence of random permutations", Journal of the American Mathematical Society, 12 (4): 1119–1178, arXiv:math/9810105, doi:10.1090/S0894-0347-99-00307-0, JSTOR 2646100, MR 1682248.

arxiv.org

Baik, Deift & Johansson (1999). Baik, J.; Deift, P.; Johansson, K. (1999), "On the distribution of the length of the longest increasing subsequence of random permutations", Journal of the American Mathematical Society, 12 (4): 1119–1178, arXiv:math/9810105, doi:10.1090/S0894-0347-99-00307-0, JSTOR 2646100, MR 1682248.
Sasamoto & Spohn (2010) Sasamoto, Tomohiro; Spohn, Herbert (2010), "One-Dimensional Kardar-Parisi-Zhang Equation: An Exact Solution and its Universality", Physical Review Letters, 104 (23): 230602, arXiv:1002.1883, Bibcode:2010PhRvL.104w0602S, doi:10.1103/PhysRevLett.104.230602, PMID 20867222, S2CID 34945972
Johansson (2000); Tracy & Widom (2009)). Johansson, K. (2000), "Shape fluctuations and random matrices", Communications in Mathematical Physics, 209 (2): 437–476, arXiv:math/9903134, Bibcode:2000CMaPh.209..437J, doi:10.1007/s002200050027, S2CID 16291076. Tracy, C. A.; Widom, H. (2009), "Asymptotics in ASEP with step initial condition", Communications in Mathematical Physics, 290 (1): 129–154, arXiv:0807.1713, Bibcode:2009CMaPh.290..129T, doi:10.1007/s00220-009-0761-0, S2CID 14730756.
Majumdar & Nechaev (2005). Majumdar, Satya N.; Nechaev, Sergei (2005), "Exact asymptotic results for the Bernoulli matching model of sequence alignment", Physical Review E, 72 (2): 020901, 4, arXiv:q-bio/0410012, Bibcode:2005PhRvE..72b0901M, doi:10.1103/PhysRevE.72.020901, MR 2177365, PMID 16196539, S2CID 11390762.
Johnstone (2007, 2008, 2009). Johnstone, I. M. (2007), "High dimensional statistical inference and random matrices" (PDF), International Congress of Mathematicians (Madrid, 2006), vol. 1, European Mathematical Society, pp. 307–333, arXiv:math/0611589, doi:10.4171/022-1/13, ISBN 978-3-98547-036-5, MR 2334195, S2CID 88524958. Johnstone, I. M. (2008), "Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy–Widom limits and rates of convergence", Annals of Statistics, 36 (6): 2638–2716, arXiv:0803.3408, doi:10.1214/08-AOS605, PMC 2821031, PMID 20157626. Johnstone, I. M. (2009), "Approximate null distribution of the largest root in multivariate analysis", Annals of Applied Statistics, 3 (4): 1616–1633, arXiv:1009.5854, doi:10.1214/08-AOAS220, PMC 2880335, PMID 20526465.
Domínguez-Molina (2017). Domínguez-Molina, J.Armando (2017), "The Tracy-Widom distribution is not infinitely divisible", Statistics & Probability Letters, 213 (1): 56–60, arXiv:1601.02898, doi:10.1016/j.spl.2016.11.029, S2CID 119676736.
Tracy & Widom (1996). Tracy, C. A.; Widom, H. (1996), "On orthogonal and symplectic matrix ensembles", Communications in Mathematical Physics, 177 (3): 727–754, arXiv:solv-int/9509007, Bibcode:1996CMaPh.177..727T, doi:10.1007/BF02099545, MR 1385083, S2CID 17398688
Majumdar, Satya N; Schehr, Grégory (2014-01-31). "Top eigenvalue of a random matrix: large deviations and third order phase transition". Journal of Statistical Mechanics: Theory and Experiment. 2014 (1): 01012. arXiv:1311.0580. Bibcode:2014JSMTE..01..012M. doi:10.1088/1742-5468/2014/01/p01012. ISSN 1742-5468. S2CID 119122520.
Baik, Deift & Johansson 1999 Baik, J.; Deift, P.; Johansson, K. (1999), "On the distribution of the length of the longest increasing subsequence of random permutations", Journal of the American Mathematical Society, 12 (4): 1119–1178, arXiv:math/9810105, doi:10.1090/S0894-0347-99-00307-0, JSTOR 2646100, MR 1682248.
Baik, Jinho; Buckingham, Robert; DiFranco, Jeffery (2008-02-26). "Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function". Communications in Mathematical Physics. 280 (2): 463–497. arXiv:0704.3636. Bibcode:2008CMaPh.280..463B. doi:10.1007/s00220-008-0433-5. ISSN 0010-3616. S2CID 16324715.
Tracy, Craig A.; Widom, Harold (May 1993). "Level-spacing distributions and the Airy kernel". Physics Letters B. 305 (1–2): 115–118. arXiv:hep-th/9210074. Bibcode:1993PhLB..305..115T. doi:10.1016/0370-2693(93)91114-3. ISSN 0370-2693. S2CID 13912236.
Amir, Gideon; Corwin, Ivan; Quastel, Jeremy (2010). "Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions". Communications on Pure and Applied Mathematics. 64 (4). Wiley: 466–537. arXiv:1003.0443. doi:10.1002/cpa.20347.

books.google.com

Bender, Carl M.; Orszag, Steven A. (1999-10-29). Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory. Springer Science & Business Media. pp. 163–165. ISBN 978-0-387-98931-0.

doi.org

Baik, Deift & Johansson (1999). Baik, J.; Deift, P.; Johansson, K. (1999), "On the distribution of the length of the longest increasing subsequence of random permutations", Journal of the American Mathematical Society, 12 (4): 1119–1178, arXiv:math/9810105, doi:10.1090/S0894-0347-99-00307-0, JSTOR 2646100, MR 1682248.
Sasamoto & Spohn (2010) Sasamoto, Tomohiro; Spohn, Herbert (2010), "One-Dimensional Kardar-Parisi-Zhang Equation: An Exact Solution and its Universality", Physical Review Letters, 104 (23): 230602, arXiv:1002.1883, Bibcode:2010PhRvL.104w0602S, doi:10.1103/PhysRevLett.104.230602, PMID 20867222, S2CID 34945972
Johansson (2000); Tracy & Widom (2009)). Johansson, K. (2000), "Shape fluctuations and random matrices", Communications in Mathematical Physics, 209 (2): 437–476, arXiv:math/9903134, Bibcode:2000CMaPh.209..437J, doi:10.1007/s002200050027, S2CID 16291076. Tracy, C. A.; Widom, H. (2009), "Asymptotics in ASEP with step initial condition", Communications in Mathematical Physics, 290 (1): 129–154, arXiv:0807.1713, Bibcode:2009CMaPh.290..129T, doi:10.1007/s00220-009-0761-0, S2CID 14730756.
Majumdar & Nechaev (2005). Majumdar, Satya N.; Nechaev, Sergei (2005), "Exact asymptotic results for the Bernoulli matching model of sequence alignment", Physical Review E, 72 (2): 020901, 4, arXiv:q-bio/0410012, Bibcode:2005PhRvE..72b0901M, doi:10.1103/PhysRevE.72.020901, MR 2177365, PMID 16196539, S2CID 11390762.
Johnstone (2007, 2008, 2009). Johnstone, I. M. (2007), "High dimensional statistical inference and random matrices" (PDF), International Congress of Mathematicians (Madrid, 2006), vol. 1, European Mathematical Society, pp. 307–333, arXiv:math/0611589, doi:10.4171/022-1/13, ISBN 978-3-98547-036-5, MR 2334195, S2CID 88524958. Johnstone, I. M. (2008), "Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy–Widom limits and rates of convergence", Annals of Statistics, 36 (6): 2638–2716, arXiv:0803.3408, doi:10.1214/08-AOS605, PMC 2821031, PMID 20157626. Johnstone, I. M. (2009), "Approximate null distribution of the largest root in multivariate analysis", Annals of Applied Statistics, 3 (4): 1616–1633, arXiv:1009.5854, doi:10.1214/08-AOAS220, PMC 2880335, PMID 20526465.
Domínguez-Molina (2017). Domínguez-Molina, J.Armando (2017), "The Tracy-Widom distribution is not infinitely divisible", Statistics & Probability Letters, 213 (1): 56–60, arXiv:1601.02898, doi:10.1016/j.spl.2016.11.029, S2CID 119676736.
Tracy, Craig A.; Widom, Harold (2009b). "The Distributions of Random Matrix Theory and their Applications". In Sidoravičius, Vladas (ed.). New Trends in Mathematical Physics. Dordrecht: Springer Netherlands. pp. 753–765. doi:10.1007/978-90-481-2810-5_48. ISBN 978-90-481-2810-5.
Forrester, P. J. (1993-08-09). "The spectrum edge of random matrix ensembles". Nuclear Physics B. 402 (3): 709–728. Bibcode:1993NuPhB.402..709F. doi:10.1016/0550-3213(93)90126-A. ISSN 0550-3213.
Tracy & Widom (1996). Tracy, C. A.; Widom, H. (1996), "On orthogonal and symplectic matrix ensembles", Communications in Mathematical Physics, 177 (3): 727–754, arXiv:solv-int/9509007, Bibcode:1996CMaPh.177..727T, doi:10.1007/BF02099545, MR 1385083, S2CID 17398688
Dieng, Momar (2005). "Distribution functions for edge eigenvalues in orthogonal and symplectic ensembles: Painlevé representations". International Mathematics Research Notices. 2005 (37): 2263–2287. doi:10.1155/IMRN.2005.2263. ISSN 1687-0247.
Majumdar, Satya N; Schehr, Grégory (2014-01-31). "Top eigenvalue of a random matrix: large deviations and third order phase transition". Journal of Statistical Mechanics: Theory and Experiment. 2014 (1): 01012. arXiv:1311.0580. Bibcode:2014JSMTE..01..012M. doi:10.1088/1742-5468/2014/01/p01012. ISSN 1742-5468. S2CID 119122520.
Baik, Deift & Johansson 1999 Baik, J.; Deift, P.; Johansson, K. (1999), "On the distribution of the length of the longest increasing subsequence of random permutations", Journal of the American Mathematical Society, 12 (4): 1119–1178, arXiv:math/9810105, doi:10.1090/S0894-0347-99-00307-0, JSTOR 2646100, MR 1682248.
Baik, Jinho; Buckingham, Robert; DiFranco, Jeffery (2008-02-26). "Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function". Communications in Mathematical Physics. 280 (2): 463–497. arXiv:0704.3636. Bibcode:2008CMaPh.280..463B. doi:10.1007/s00220-008-0433-5. ISSN 0010-3616. S2CID 16324715.
Tracy, Craig A.; Widom, Harold (May 1993). "Level-spacing distributions and the Airy kernel". Physics Letters B. 305 (1–2): 115–118. arXiv:hep-th/9210074. Bibcode:1993PhLB..305..115T. doi:10.1016/0370-2693(93)91114-3. ISSN 0370-2693. S2CID 13912236.
Su, Zhong-gen; Lei, Yu-huan; Shen, Tian (2021-03-01). "Tracy-Widom distribution, Airy2 process and its sample path properties". Applied Mathematics-A Journal of Chinese Universities. 36 (1): 128–158. doi:10.1007/s11766-021-4251-2. ISSN 1993-0445. S2CID 237903590.
Amir, Gideon; Corwin, Ivan; Quastel, Jeremy (2010). "Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions". Communications on Pure and Applied Mathematics. 64 (4). Wiley: 466–537. arXiv:1003.0443. doi:10.1002/cpa.20347.

dx.doi.org

Forrester, P. J. (1993-08-09). "The spectrum edge of random matrix ensembles". Nuclear Physics B. 402 (3): 709–728. Bibcode:1993NuPhB.402..709F. doi:10.1016/0550-3213(93)90126-A. ISSN 0550-3213.
Majumdar, Satya N; Schehr, Grégory (2014-01-31). "Top eigenvalue of a random matrix: large deviations and third order phase transition". Journal of Statistical Mechanics: Theory and Experiment. 2014 (1): 01012. arXiv:1311.0580. Bibcode:2014JSMTE..01..012M. doi:10.1088/1742-5468/2014/01/p01012. ISSN 1742-5468. S2CID 119122520.
Baik, Jinho; Buckingham, Robert; DiFranco, Jeffery (2008-02-26). "Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function". Communications in Mathematical Physics. 280 (2): 463–497. arXiv:0704.3636. Bibcode:2008CMaPh.280..463B. doi:10.1007/s00220-008-0433-5. ISSN 0010-3616. S2CID 16324715.
Tracy, Craig A.; Widom, Harold (May 1993). "Level-spacing distributions and the Airy kernel". Physics Letters B. 305 (1–2): 115–118. arXiv:hep-th/9210074. Bibcode:1993PhLB..305..115T. doi:10.1016/0370-2693(93)91114-3. ISSN 0370-2693. S2CID 13912236.

harvard.edu

ui.adsabs.harvard.edu

Sasamoto & Spohn (2010) Sasamoto, Tomohiro; Spohn, Herbert (2010), "One-Dimensional Kardar-Parisi-Zhang Equation: An Exact Solution and its Universality", Physical Review Letters, 104 (23): 230602, arXiv:1002.1883, Bibcode:2010PhRvL.104w0602S, doi:10.1103/PhysRevLett.104.230602, PMID 20867222, S2CID 34945972
Johansson (2000); Tracy & Widom (2009)). Johansson, K. (2000), "Shape fluctuations and random matrices", Communications in Mathematical Physics, 209 (2): 437–476, arXiv:math/9903134, Bibcode:2000CMaPh.209..437J, doi:10.1007/s002200050027, S2CID 16291076. Tracy, C. A.; Widom, H. (2009), "Asymptotics in ASEP with step initial condition", Communications in Mathematical Physics, 290 (1): 129–154, arXiv:0807.1713, Bibcode:2009CMaPh.290..129T, doi:10.1007/s00220-009-0761-0, S2CID 14730756.
Majumdar & Nechaev (2005). Majumdar, Satya N.; Nechaev, Sergei (2005), "Exact asymptotic results for the Bernoulli matching model of sequence alignment", Physical Review E, 72 (2): 020901, 4, arXiv:q-bio/0410012, Bibcode:2005PhRvE..72b0901M, doi:10.1103/PhysRevE.72.020901, MR 2177365, PMID 16196539, S2CID 11390762.
Forrester, P. J. (1993-08-09). "The spectrum edge of random matrix ensembles". Nuclear Physics B. 402 (3): 709–728. Bibcode:1993NuPhB.402..709F. doi:10.1016/0550-3213(93)90126-A. ISSN 0550-3213.
Tracy & Widom (1996). Tracy, C. A.; Widom, H. (1996), "On orthogonal and symplectic matrix ensembles", Communications in Mathematical Physics, 177 (3): 727–754, arXiv:solv-int/9509007, Bibcode:1996CMaPh.177..727T, doi:10.1007/BF02099545, MR 1385083, S2CID 17398688
Majumdar, Satya N; Schehr, Grégory (2014-01-31). "Top eigenvalue of a random matrix: large deviations and third order phase transition". Journal of Statistical Mechanics: Theory and Experiment. 2014 (1): 01012. arXiv:1311.0580. Bibcode:2014JSMTE..01..012M. doi:10.1088/1742-5468/2014/01/p01012. ISSN 1742-5468. S2CID 119122520.
Baik, Jinho; Buckingham, Robert; DiFranco, Jeffery (2008-02-26). "Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function". Communications in Mathematical Physics. 280 (2): 463–497. arXiv:0704.3636. Bibcode:2008CMaPh.280..463B. doi:10.1007/s00220-008-0433-5. ISSN 0010-3616. S2CID 16324715.
Tracy, Craig A.; Widom, Harold (May 1993). "Level-spacing distributions and the Airy kernel". Physics Letters B. 305 (1–2): 115–118. arXiv:hep-th/9210074. Bibcode:1993PhLB..305..115T. doi:10.1016/0370-2693(93)91114-3. ISSN 0370-2693. S2CID 13912236.

icm2006.org

Johnstone (2007, 2008, 2009). Johnstone, I. M. (2007), "High dimensional statistical inference and random matrices" (PDF), International Congress of Mathematicians (Madrid, 2006), vol. 1, European Mathematical Society, pp. 307–333, arXiv:math/0611589, doi:10.4171/022-1/13, ISBN 978-3-98547-036-5, MR 2334195, S2CID 88524958. Johnstone, I. M. (2008), "Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy–Widom limits and rates of convergence", Annals of Statistics, 36 (6): 2638–2716, arXiv:0803.3408, doi:10.1214/08-AOS605, PMC 2821031, PMID 20157626. Johnstone, I. M. (2009), "Approximate null distribution of the largest root in multivariate analysis", Annals of Applied Statistics, 3 (4): 1616–1633, arXiv:1009.5854, doi:10.1214/08-AOAS220, PMC 2880335, PMID 20526465.

jstor.org

Baik, Deift & Johansson (1999). Baik, J.; Deift, P.; Johansson, K. (1999), "On the distribution of the length of the longest increasing subsequence of random permutations", Journal of the American Mathematical Society, 12 (4): 1119–1178, arXiv:math/9810105, doi:10.1090/S0894-0347-99-00307-0, JSTOR 2646100, MR 1682248.
Baik, Deift & Johansson 1999 Baik, J.; Deift, P.; Johansson, K. (1999), "On the distribution of the length of the longest increasing subsequence of random permutations", Journal of the American Mathematical Society, 12 (4): 1119–1178, arXiv:math/9810105, doi:10.1090/S0894-0347-99-00307-0, JSTOR 2646100, MR 1682248.

nih.gov

pubmed.ncbi.nlm.nih.gov

Sasamoto & Spohn (2010) Sasamoto, Tomohiro; Spohn, Herbert (2010), "One-Dimensional Kardar-Parisi-Zhang Equation: An Exact Solution and its Universality", Physical Review Letters, 104 (23): 230602, arXiv:1002.1883, Bibcode:2010PhRvL.104w0602S, doi:10.1103/PhysRevLett.104.230602, PMID 20867222, S2CID 34945972
Majumdar & Nechaev (2005). Majumdar, Satya N.; Nechaev, Sergei (2005), "Exact asymptotic results for the Bernoulli matching model of sequence alignment", Physical Review E, 72 (2): 020901, 4, arXiv:q-bio/0410012, Bibcode:2005PhRvE..72b0901M, doi:10.1103/PhysRevE.72.020901, MR 2177365, PMID 16196539, S2CID 11390762.
Johnstone (2007, 2008, 2009). Johnstone, I. M. (2007), "High dimensional statistical inference and random matrices" (PDF), International Congress of Mathematicians (Madrid, 2006), vol. 1, European Mathematical Society, pp. 307–333, arXiv:math/0611589, doi:10.4171/022-1/13, ISBN 978-3-98547-036-5, MR 2334195, S2CID 88524958. Johnstone, I. M. (2008), "Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy–Widom limits and rates of convergence", Annals of Statistics, 36 (6): 2638–2716, arXiv:0803.3408, doi:10.1214/08-AOS605, PMC 2821031, PMID 20157626. Johnstone, I. M. (2009), "Approximate null distribution of the largest root in multivariate analysis", Annals of Applied Statistics, 3 (4): 1616–1633, arXiv:1009.5854, doi:10.1214/08-AOAS220, PMC 2880335, PMID 20526465.

ncbi.nlm.nih.gov

Johnstone (2007, 2008, 2009). Johnstone, I. M. (2007), "High dimensional statistical inference and random matrices" (PDF), International Congress of Mathematicians (Madrid, 2006), vol. 1, European Mathematical Society, pp. 307–333, arXiv:math/0611589, doi:10.4171/022-1/13, ISBN 978-3-98547-036-5, MR 2334195, S2CID 88524958. Johnstone, I. M. (2008), "Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy–Widom limits and rates of convergence", Annals of Statistics, 36 (6): 2638–2716, arXiv:0803.3408, doi:10.1214/08-AOS605, PMC 2821031, PMID 20157626. Johnstone, I. M. (2009), "Approximate null distribution of the largest root in multivariate analysis", Annals of Applied Statistics, 3 (4): 1616–1633, arXiv:1009.5854, doi:10.1214/08-AOAS220, PMC 2880335, PMID 20526465.

semanticscholar.org

api.semanticscholar.org

Sasamoto & Spohn (2010) Sasamoto, Tomohiro; Spohn, Herbert (2010), "One-Dimensional Kardar-Parisi-Zhang Equation: An Exact Solution and its Universality", Physical Review Letters, 104 (23): 230602, arXiv:1002.1883, Bibcode:2010PhRvL.104w0602S, doi:10.1103/PhysRevLett.104.230602, PMID 20867222, S2CID 34945972
Johansson (2000); Tracy & Widom (2009)). Johansson, K. (2000), "Shape fluctuations and random matrices", Communications in Mathematical Physics, 209 (2): 437–476, arXiv:math/9903134, Bibcode:2000CMaPh.209..437J, doi:10.1007/s002200050027, S2CID 16291076. Tracy, C. A.; Widom, H. (2009), "Asymptotics in ASEP with step initial condition", Communications in Mathematical Physics, 290 (1): 129–154, arXiv:0807.1713, Bibcode:2009CMaPh.290..129T, doi:10.1007/s00220-009-0761-0, S2CID 14730756.
Majumdar & Nechaev (2005). Majumdar, Satya N.; Nechaev, Sergei (2005), "Exact asymptotic results for the Bernoulli matching model of sequence alignment", Physical Review E, 72 (2): 020901, 4, arXiv:q-bio/0410012, Bibcode:2005PhRvE..72b0901M, doi:10.1103/PhysRevE.72.020901, MR 2177365, PMID 16196539, S2CID 11390762.
Johnstone (2007, 2008, 2009). Johnstone, I. M. (2007), "High dimensional statistical inference and random matrices" (PDF), International Congress of Mathematicians (Madrid, 2006), vol. 1, European Mathematical Society, pp. 307–333, arXiv:math/0611589, doi:10.4171/022-1/13, ISBN 978-3-98547-036-5, MR 2334195, S2CID 88524958. Johnstone, I. M. (2008), "Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy–Widom limits and rates of convergence", Annals of Statistics, 36 (6): 2638–2716, arXiv:0803.3408, doi:10.1214/08-AOS605, PMC 2821031, PMID 20157626. Johnstone, I. M. (2009), "Approximate null distribution of the largest root in multivariate analysis", Annals of Applied Statistics, 3 (4): 1616–1633, arXiv:1009.5854, doi:10.1214/08-AOAS220, PMC 2880335, PMID 20526465.
Domínguez-Molina (2017). Domínguez-Molina, J.Armando (2017), "The Tracy-Widom distribution is not infinitely divisible", Statistics & Probability Letters, 213 (1): 56–60, arXiv:1601.02898, doi:10.1016/j.spl.2016.11.029, S2CID 119676736.
Tracy & Widom (1996). Tracy, C. A.; Widom, H. (1996), "On orthogonal and symplectic matrix ensembles", Communications in Mathematical Physics, 177 (3): 727–754, arXiv:solv-int/9509007, Bibcode:1996CMaPh.177..727T, doi:10.1007/BF02099545, MR 1385083, S2CID 17398688
Majumdar, Satya N; Schehr, Grégory (2014-01-31). "Top eigenvalue of a random matrix: large deviations and third order phase transition". Journal of Statistical Mechanics: Theory and Experiment. 2014 (1): 01012. arXiv:1311.0580. Bibcode:2014JSMTE..01..012M. doi:10.1088/1742-5468/2014/01/p01012. ISSN 1742-5468. S2CID 119122520.
Baik, Jinho; Buckingham, Robert; DiFranco, Jeffery (2008-02-26). "Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function". Communications in Mathematical Physics. 280 (2): 463–497. arXiv:0704.3636. Bibcode:2008CMaPh.280..463B. doi:10.1007/s00220-008-0433-5. ISSN 0010-3616. S2CID 16324715.
Tracy, Craig A.; Widom, Harold (May 1993). "Level-spacing distributions and the Airy kernel". Physics Letters B. 305 (1–2): 115–118. arXiv:hep-th/9210074. Bibcode:1993PhLB..305..115T. doi:10.1016/0370-2693(93)91114-3. ISSN 0370-2693. S2CID 13912236.
Su, Zhong-gen; Lei, Yu-huan; Shen, Tian (2021-03-01). "Tracy-Widom distribution, Airy2 process and its sample path properties". Applied Mathematics-A Journal of Chinese Universities. 36 (1): 128–158. doi:10.1007/s11766-021-4251-2. ISSN 1993-0445. S2CID 237903590.

springer.com

link.springer.com

Tracy, Craig A.; Widom, Harold (2009b). "The Distributions of Random Matrix Theory and their Applications". In Sidoravičius, Vladas (ed.). New Trends in Mathematical Physics. Dordrecht: Springer Netherlands. pp. 753–765. doi:10.1007/978-90-481-2810-5_48. ISBN 978-90-481-2810-5.

wired.com

Mysterious Statistical Law May Finally Have an Explanation, wired.com 2014-10-27

worldcat.org

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Forrester, P. J. (1993-08-09). "The spectrum edge of random matrix ensembles". Nuclear Physics B. 402 (3): 709–728. Bibcode:1993NuPhB.402..709F. doi:10.1016/0550-3213(93)90126-A. ISSN 0550-3213.
Dieng, Momar (2005). "Distribution functions for edge eigenvalues in orthogonal and symplectic ensembles: Painlevé representations". International Mathematics Research Notices. 2005 (37): 2263–2287. doi:10.1155/IMRN.2005.2263. ISSN 1687-0247.
Majumdar, Satya N; Schehr, Grégory (2014-01-31). "Top eigenvalue of a random matrix: large deviations and third order phase transition". Journal of Statistical Mechanics: Theory and Experiment. 2014 (1): 01012. arXiv:1311.0580. Bibcode:2014JSMTE..01..012M. doi:10.1088/1742-5468/2014/01/p01012. ISSN 1742-5468. S2CID 119122520.
Baik, Jinho; Buckingham, Robert; DiFranco, Jeffery (2008-02-26). "Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function". Communications in Mathematical Physics. 280 (2): 463–497. arXiv:0704.3636. Bibcode:2008CMaPh.280..463B. doi:10.1007/s00220-008-0433-5. ISSN 0010-3616. S2CID 16324715.
Tracy, Craig A.; Widom, Harold (May 1993). "Level-spacing distributions and the Airy kernel". Physics Letters B. 305 (1–2): 115–118. arXiv:hep-th/9210074. Bibcode:1993PhLB..305..115T. doi:10.1016/0370-2693(93)91114-3. ISSN 0370-2693. S2CID 13912236.
Su, Zhong-gen; Lei, Yu-huan; Shen, Tian (2021-03-01). "Tracy-Widom distribution, Airy2 process and its sample path properties". Applied Mathematics-A Journal of Chinese Universities. 36 (1): 128–158. doi:10.1007/s11766-021-4251-2. ISSN 1993-0445. S2CID 237903590.