References analysis of the Wikipedia article "List of probabilistic proofs of non-probabilistic theorems" in the English version

arxiv.org

Markowsky, Greg T. (2011), "On the expected exit time of planar Brownian motion from simply connected domains", Electronic Communications in Probability, 16: 652–663, arXiv:1108.1188, doi:10.1214/ecp.v16-1653, S2CID 55705658.

Abért, Miklós; Weiss, Benjamin (2011). "Bernoulli actions are weakly contained in any free action". arXiv:1103.1063v2 [math.DS].

Tolsa, Xavier; Volberg, Alexander (2017). "On Tsirelson's theorem about triple points for harmonic measure". International Mathematics Research Notices. 2018 (12): 3671–3683. arXiv:1608.04022. doi:10.1093/imrn/rnw345.

Horowitz, Charles; Usadi Katz, Karin; Katz, Mikhail G. (2008). "Loewner's torus inequality with isosystolic defect". Journal of Geometric Analysis. 19 (4): 796–808. arXiv:0803.0690. doi:10.1007/s12220-009-9090-y. S2CID 18444111.

Neel, Robert W. (2008), "A martingale approach to minimal surfaces", Journal of Functional Analysis, 256 (8), Elsevier: 2440–2472, arXiv:0805.0556, doi:10.1016/j.jfa.2008.06.033, S2CID 15228691. Also arXiv:0805.0556.

Fulman, Jason (2001), "A probabilistic proof of the Rogers–Ramanujan identities", Bulletin of the London Mathematical Society, 33 (4): 397–407, arXiv:math/0001078, doi:10.1017/S0024609301008207, S2CID 673691, archived from the original on 2012-07-07. Also arXiv:math.CO/0001078.

Tsirelson, Boris (2003), "Non-isomorphic product systems", in Price, Geoffrey (ed.), Advances in quantum dynamics, Contemporary mathematics, vol. 335, American mathematical society, pp. 273–328, ISBN 0-8218-3215-8. Also arXiv:math.FA/0210457.

Bhat, B.V.Rajarama; Srinivasan, Raman (2005), "On product systems arising from sum systems", Infinite Dimensional Analysis, Quantum Probability and Related Topics, 8 (1): 1–31, arXiv:math/0405276, doi:10.1142/S0219025705001834, S2CID 15106610. Also arXiv:math.OA/0405276.

Izumi, Masaki; Srinivasan, Raman (2008), "Generalized CCR flows", Communications in Mathematical Physics, 281 (2): 529–571, arXiv:0705.3280, Bibcode:2008CMaPh.281..529I, doi:10.1007/s00220-008-0447-z, S2CID 12815055. Also arXiv:0705.3280.

Perez-Garcia, D.; Wolf, M.M.; C., Palazuelos; Villanueva, I.; Junge, M. (2008), "Unbounded violation of tripartite Bell inequalities", Communications in Mathematical Physics, 279 (2): 455–486, arXiv:quant-ph/0702189, Bibcode:2008CMaPh.279..455P, doi:10.1007/s00220-008-0418-4, S2CID 29110154

doi.org

Salem, Raphaël (1951). "On singular monotonic functions whose spectrum has a given Hausdorff dimension". Ark. Mat. 1 (4): 353–365. Bibcode:1951ArM.....1..353S. doi:10.1007/bf02591372.

Kaufman, Robert (1981). "On the theorem of Jarník and Besicovitch". Acta Arith. 39 (3): 265–267. doi:10.4064/aa-39-3-265-267.

Blyth, Colin R.; Pathak, Pramod K. (1986), "A note on easy proofs of Stirling's theorem", American Mathematical Monthly, 93 (5): 376–379, doi:10.2307/2323600, JSTOR 2323600.

Gordon, Louis (1994), "A stochastic approach to the gamma function", American Mathematical Monthly, 101 (9): 858–865, doi:10.2307/2975134, JSTOR 2975134.

Davis, Burgess (1975), "Picard's theorem and Brownian motion", Transactions of the American Mathematical Society, 213: 353–362, doi:10.2307/1998050, JSTOR 1998050.

Davis, Burgess (1979), "Brownian motion and analytic functions", Annals of Probability, 7 (6): 913–932, doi:10.1214/aop/1176994888.

Wong, T.K.; Yam, S.C.P. (2018), "A probabilistic proof for Fourier inversion formula", Statistics & Probability Letters, 141: 135–142, doi:10.1016/j.spl.2018.05.028, S2CID 125351871.

Bismut, Jean-Michel (1984), "The Atiyah–Singer Theorems: A Probabilistic Approach. I. The index theorem", J. Funct. Anal., 57: 56–99, doi:10.1016/0022-1236(84)90101-0.

Bishop, C. (1991), "A characterization of Poissonian domains", Arkiv för Matematik, 29 (1): 1–24, Bibcode:1991ArM....29....1B, doi:10.1007/BF02384328 (see Section 6).

Tsirelson, Boris (1997), "Triple points: from non-Brownian filtrations to harmonic measures", Geometric and Functional Analysis, 7 (6), Birkhauser: 1096–1142, doi:10.1007/s000390050038, S2CID 121617197. author's site

harvard.edu

ui.adsabs.harvard.edu

Salem, Raphaël (1951). "On singular monotonic functions whose spectrum has a given Hausdorff dimension". Ark. Mat. 1 (4): 353–365. Bibcode:1951ArM.....1..353S. doi:10.1007/bf02591372.

Bishop, C. (1991), "A characterization of Poissonian domains", Arkiv för Matematik, 29 (1): 1–24, Bibcode:1991ArM....29....1B, doi:10.1007/BF02384328 (see Section 6).

jstor.org

Blyth, Colin R.; Pathak, Pramod K. (1986), "A note on easy proofs of Stirling's theorem", American Mathematical Monthly, 93 (5): 376–379, doi:10.2307/2323600, JSTOR 2323600.

Gordon, Louis (1994), "A stochastic approach to the gamma function", American Mathematical Monthly, 101 (9): 858–865, doi:10.2307/2975134, JSTOR 2975134.

Davis, Burgess (1975), "Picard's theorem and Brownian motion", Transactions of the American Mathematical Society, 213: 353–362, doi:10.2307/1998050, JSTOR 1998050.

semanticscholar.org

api.semanticscholar.org

Wong, T.K.; Yam, S.C.P. (2018), "A probabilistic proof for Fourier inversion formula", Statistics & Probability Letters, 141: 135–142, doi:10.1016/j.spl.2018.05.028, S2CID 125351871.

uni-bielefeld.de

mathematik.uni-bielefeld.de

Tsirelson, Boris (1998), "Within and beyond the reach of Brownian innovation", Proceedings of the international congress of mathematicians, Documenta mathematica, vol. Extra Volume ICM 1998, III, Berlin: der Deutschen Mathematiker-Vereinigung, pp. 311–320, ISSN 1431-0635.

List of probabilistic proofs of non-probabilistic theorems (English Wikipedia)

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