Commentary on “Longest increasing subsequences: from patience sorting to the Baik–Deift–Johansson theorem” by David Aldous and Persi Diaconis
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Abstract:
Immediately following the commentary below, this previously published article is reprinted in its entirety: David Aldous and Persi Diaconis, “Longest increasing subsequences: from patience sorting to the Baik–Deift–Johansson theorem”, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 4, 413–432.References
- David Aldous and Persi Diaconis, Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 4, 413–432. MR 1694204, DOI 10.1090/S0273-0979-99-00796-X
- Greg W. Anderson, Alice Guionnet, and Ofer Zeitouni, An introduction to random matrices, Cambridge Studies in Advanced Mathematics, vol. 118, Cambridge University Press, Cambridge, 2010. MR 2760897
- Jinho Baik, Percy Deift, and Kurt Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, J. Amer. Math. Soc. 12 (1999), no. 4, 1119–1178. MR 1682248, DOI 10.1090/S0894-0347-99-00307-0
- Jinho Baik, Percy Deift, and Toufic Suidan, Combinatorics and random matrix theory, Graduate Studies in Mathematics, vol. 172, American Mathematical Society, Providence, RI, 2016. MR 3468920, DOI 10.1090/gsm/172
- Márton Balázs and Timo Seppäläinen, Order of current variance and diffusivity in the asymmetric simple exclusion process, Ann. of Math. (2) 171 (2010), no. 2, 1237–1265. MR 2630064, DOI 10.4007/annals.2010.171.1237
- Rodney J. Baxter, Exactly solved models in statistical mechanics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1982. MR 690578
- Lorenzo Bertini and Nicoletta Cancrini, The stochastic heat equation: Feynman-Kac formula and intermittence, J. Statist. Phys. 78 (1995), no. 5-6, 1377–1401. MR 1316109, DOI 10.1007/BF02180136
- Lorenzo Bertini and Giambattista Giacomin, Stochastic Burgers and KPZ equations from particle systems, Comm. Math. Phys. 183 (1997), no. 3, 571–607. MR 1462228, DOI 10.1007/s002200050044
- Alexei Borodin and Ivan Corwin, Macdonald processes, Probab. Theory Related Fields 158 (2014), no. 1-2, 225–400. MR 3152785, DOI 10.1007/s00440-013-0482-3
- Alexei Borodin, Ivan Corwin, and Patrik Ferrari, Free energy fluctuations for directed polymers in random media in $1+1$ dimension, Comm. Pure Appl. Math. 67 (2014), no. 7, 1129–1214. MR 3207195, DOI 10.1002/cpa.21520
- Alexei Borodin and Patrik L. Ferrari, Anisotropic growth of random surfaces in $2+1$ dimensions, Comm. Math. Phys. 325 (2014), no. 2, 603–684. MR 3148098, DOI 10.1007/s00220-013-1823-x
- Alexei Borodin and Vadim Gorin, Lectures on integrable probability, Probability and statistical physics in St. Petersburg, Proc. Sympos. Pure Math., vol. 91, Amer. Math. Soc., Providence, RI, 2016, pp. 155–214. MR 3526828, DOI 10.1007/s00029-010-0034-y
- Alexei Borodin and Leonid Petrov, Integrable probability: from representation theory to Macdonald processes, Probab. Surv. 11 (2014), 1–58. MR 3178541, DOI 10.1214/13-PS225
- Alexei Borodin and Leonid Petrov, Integrable probability: stochastic vertex models and symmetric functions, Stochastic processes and random matrices, Oxford Univ. Press, Oxford, 2017, pp. 26–131. MR 3728714
- Alexei Borodin and Grigori Olshanski, Representations of the infinite symmetric group, Cambridge Studies in Advanced Mathematics, vol. 160, Cambridge University Press, Cambridge, 2017. MR 3618143, DOI 10.1017/CBO9781316798577
- Gioia Carinci, Cristian Giardinà, Frank Redig, and Tomohiro Sasamoto, A generalized asymmetric exclusion process with $U_q(\mathfrak {sl}_2)$ stochastic duality, Probab. Theory Related Fields 166 (2016), no. 3-4, 887–933. MR 3568042, DOI 10.1007/s00440-015-0674-0
- Ivan Corwin, The Kardar-Parisi-Zhang equation and universality class, Random Matrices Theory Appl. 1 (2012), no. 1, 1130001, 76. MR 2930377, DOI 10.1142/S2010326311300014
- I. Corwin, Kardar-Parisi-Zhang universality, Notices Amer. Math. Soc. 63 (2016), no. 3, 230–239. MR 3445162, DOI 10.1090/noti1334
- Ivan Corwin and Leonid Petrov, Stochastic higher spin vertex models on the line, Comm. Math. Phys. 343 (2016), no. 2, 651–700. MR 3477349, DOI 10.1007/s00220-015-2479-5
- Ivan Corwin, Jeremy Quastel, and Daniel Remenik, Renormalization fixed point of the KPZ universality class, J. Stat. Phys. 160 (2015), no. 4, 815–834. MR 3373642, DOI 10.1007/s10955-015-1243-8
- Amir Dembo and Li-Cheng Tsai, Weakly asymmetric non-simple exclusion process and the Kardar-Parisi-Zhang equation, Comm. Math. Phys. 341 (2016), no. 1, 219–261. MR 3439226, DOI 10.1007/s00220-015-2527-1
- Gernot Akemann, Jinho Baik, and Philippe Di Francesco (eds.), The Oxford handbook of random matrix theory, Oxford University Press, Oxford, 2011. MR 2920518
- Athanassios S. Fokas, Alexander R. Its, Andrei A. Kapaev, and Victor Yu. Novokshenov, Painlevé transcendents, Mathematical Surveys and Monographs, vol. 128, American Mathematical Society, Providence, RI, 2006. The Riemann-Hilbert approach. MR 2264522, DOI 10.1090/surv/128
- P. J. Forrester, Log-gases and random matrices, London Mathematical Society Monographs Series, vol. 34, Princeton University Press, Princeton, NJ, 2010. MR 2641363, DOI 10.1515/9781400835416
- P. Goncalves and M. Jara, Universality of KPZ equation, arXiv:1003.4478, 2010.
- Patrícia Gonçalves, Milton Jara, and Sunder Sethuraman, A stochastic Burgers equation from a class of microscopic interactions, Ann. Probab. 43 (2015), no. 1, 286–338. MR 3298474, DOI 10.1214/13-AOP878
- Massimiliano Gubinelli, Peter Imkeller, and Nicolas Perkowski, Paracontrolled distributions and singular PDEs, Forum Math. Pi 3 (2015), e6, 75. MR 3406823, DOI 10.1017/fmp.2015.2
- Massimiliano Gubinelli and Nicolas Perkowski, KPZ reloaded, Comm. Math. Phys. 349 (2017), no. 1, 165–269. MR 3592748, DOI 10.1007/s00220-016-2788-3
- Massimiliano Gubinelli and Nicolas Perkowski, Energy solutions of KPZ are unique, J. Amer. Math. Soc. 31 (2018), no. 2, 427–471. MR 3758149, DOI 10.1090/jams/889
- Martin Hairer, Solving the KPZ equation, Ann. of Math. (2) 178 (2013), no. 2, 559–664. MR 3071506, DOI 10.4007/annals.2013.178.2.4
- M. Hairer, A theory of regularity structures, Invent. Math. 198 (2014), no. 2, 269–504. MR 3274562, DOI 10.1007/s00222-014-0505-4
- M. Hairer and J. Quastel, A class of growth models rescaling to KPZ, arXiv:1512.07845, 2015.
- Martin Hairer and Hao Shen, A central limit theorem for the KPZ equation, Ann. Probab. 45 (2017), no. 6B, 4167–4221. MR 3737909, DOI 10.1214/16-AOP1162
- Timothy Halpin-Healy and Kazumasa A. Takeuchi, A KPZ cocktail—shaken, not stirred …toasting 30 years of kinetically roughened surfaces, J. Stat. Phys. 160 (2015), no. 4, 794–814. MR 3373641, DOI 10.1007/s10955-015-1282-1
- K. Kardar, G. Parisi, Y. Z. Zhang, Dynamic scaling of growing interfaces, Phys. Rev. Lett., 56 (1986), 889–892.
- S. V. Kerov, Asymptotic representation theory of the symmetric group and its applications in analysis, Translations of Mathematical Monographs, vol. 219, American Mathematical Society, Providence, RI, 2003. Translated from the Russian manuscript by N. V. Tsilevich; With a foreword by A. Vershik and comments by G. Olshanski. MR 1984868, DOI 10.1090/mmono/219
- V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum inverse scattering method and correlation functions, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1993. MR 1245942, DOI 10.1017/CBO9780511628832
- J. Krug and H. Spohn, Kinetic Roughening of Growing Interfaces, Solids far from Equilibrium: Growth, Morphology and Defects, pp. 479–582, Cambridge University Press, 1992.
- Antti Kupiainen, Renormalization group and stochastic PDEs, Ann. Henri Poincaré 17 (2016), no. 3, 497–535. MR 3459120, DOI 10.1007/s00023-015-0408-y
- I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. With contributions by A. Zelevinsky; Oxford Science Publications. MR 1354144
- K. Matetski, J. Quastel, and D. Remenik, The KPZ fixed point, arXiv:1701.00018, 2017.
- Neil O’Connell, Whittaker functions and related stochastic processes, Random matrix theory, interacting particle systems, and integrable systems, Math. Sci. Res. Inst. Publ., vol. 65, Cambridge Univ. Press, New York, 2014, pp. 385–409. MR 3380693
- Andrei Okounkov, Infinite wedge and random partitions, Selecta Math. (N.S.) 7 (2001), no. 1, 57–81. MR 1856553, DOI 10.1007/PL00001398
- Jeremy Quastel, Introduction to KPZ, Current developments in mathematics, 2011, Int. Press, Somerville, MA, 2012, pp. 125–194. MR 3098078
- Jeremy Quastel and Herbert Spohn, The one-dimensional KPZ equation and its universality class, J. Stat. Phys. 160 (2015), no. 4, 965–984. MR 3373647, DOI 10.1007/s10955-015-1250-9
- Jeremy Quastel and Benedek Valko, $t^{1/3}$ Superdiffusivity of finite-range asymmetric exclusion processes on $\Bbb Z$, Comm. Math. Phys. 273 (2007), no. 2, 379–394. MR 2318311, DOI 10.1007/s00220-007-0242-2
- Dan Romik, The surprising mathematics of longest increasing subsequences, Institute of Mathematical Statistics Textbooks, vol. 4, Cambridge University Press, New York, 2015. MR 3468738
- Gunter M. Schütz, Duality relations for asymmetric exclusion processes, J. Statist. Phys. 86 (1997), no. 5-6, 1265–1287. MR 1450767, DOI 10.1007/BF02183623
- Craig A. Tracy and Harold Widom, Level-spacing distributions and the Airy kernel, Comm. Math. Phys. 159 (1994), no. 1, 151–174. MR 1257246, DOI 10.1007/BF02100489
- Craig A. Tracy and Harold Widom, Asymptotics in ASEP with step initial condition, Comm. Math. Phys. 290 (2009), no. 1, 129–154. MR 2520510, DOI 10.1007/s00220-009-0761-0
Additional Information
- Ivan Corwin
- Affiliation: Columbia University, Department of Mathematics, 2990 Broadway, New York, New York
- MR Author ID: 833613
- Email: ivan.corwin@gmail.com
- Received by editor(s): April 7, 2018
- Published electronically: April 18, 2018
- Additional Notes: The author recognizes partial NSF support from DMS-1664650, as well as support from a Packard Foundation Fellowship for Science and Engineering.
- © Copyright 2018 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 55 (2018), 363-374
- MSC (2010): Primary 82C22, 60H15
- DOI: https://doi.org/10.1090/bull/1623
- MathSciNet review: 3803162