Yuri Bakhtin. 
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Yuri Bakhtin

Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University

Research interests: random dynamics, probabilistic models of mathematical physics

A link for students wishing to email me

Office: CI/WWH 713

  • Yuri Bakhtin, Tobias Hurth, Sean D. Lawley, Jonathan C. Mattingly, Singularities of invariant densities for random switching between two linear ODEs in 2D. https://arxiv.org/abs/2009.01299
  • Yuri Bakhtin, Mikhail I. Katsnelson, Yuri I. Wolf, Eugene V. Koonin Punctuated equilibrium as the default mode of evolution of large populations on fitness landscapes dominated by saddle points in the weak-mutation limit https://arxiv.org/abs/2007.10228 25 pp
  • Yuri Bakhtin, Hong-Bin Chen, Atypical exit events near a repelling equilibrium https://arxiv.org/abs/1911.06437 29pp, accepted at Annals of Probability
  • Yuri Bakhtin, Hong-Bin Chen, Long exit times near a repelling equilibrium https://arxiv.org/abs/1908.11840 29pp, accepted at Annals of Applied Probability
  • Yuri Bakhtin, Donghyun Seo, Localization of directed polymers in continuous space https://arxiv.org/abs/1905.00930 56pp, accepted at Electronic Journal of Probability
  • Yuri Bakhtin, Liying Li, Strongly mixing smooth planar vector field without asymptotic directions https://arxiv.org/abs/1903.02733 22pp
  • Yuri Bakhtin, Liying Li, Weakly mixing smooth planar vector field without asymptotic directions https://arxiv.org/abs/1808.05544, Proc. Amer. Math. Soc. 148 (2020), 4733-4744
  • Yuri Bakhtin, Zsolt Pajor-Gyulai, Tails of exit times from unstable equilibria on the line https://arxiv.org/abs/1810.05341 Journal of Applied Probability, Volume 57, Issue 2 June 2020 , pp. 477-496
  • Yuri Bakhtin, Alexisz Gaál, Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium https://arxiv.org/abs/1901.05513, Stochastics and Dynamics Vol. 20, No. 04, 2050026 (2020)
  • Yuri Bakhtin, Zsolt Pajor-Gyulai, Scaling limit for escapes from unstable equilibria in the vanishing noise limit: nontrivial Jordan block case https://arxiv.org/abs/1708.00558 Stochastics and Dynamics Vol. 18, No. 5 (2019) 1950022 (21 pages)
  • Yuri Bakhtin, Wei Wu, Transversal fluctuations for a first passage percolation model http://arxiv.org/abs/1605.05965 Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, Volume 55, Number 2 (2019), 1042-1060
  • Yuri Bakhtin, Universal statistics of incubation periods and other detection times via diffusion models https://arxiv.org/abs/1804.05961 Bulletin of Mathematical Biology, Volume 81 (2019), Issue 4, pp 1070–1088
  • Yuri Bakhtin, Zsolt Pajor-Gyulai, Malliavin calculus approach to long exit times from an unstable equilibrium, https://arxiv.org/abs/1710.03293 Annals of Applied Probability (2019) Vol. 29, No. 2, 827-850
  • Yuri Bakhtin, Liying Li, Thermodynamic limit for directed polymers and stationary solutions of the Burgers equation http://arxiv.org/abs/1607.04864Comm. Pure Appl. Math., 72 (2019): pp.536-619
  • Yuri Bakhtin, Liying Li, Zero temperature limit for directed polymers and inviscid limit for stationary solutions of stochastic Burgers equation https://arxiv.org/abs/1706.09950 Journal of Statistical Physics, 172 (2018), Issue 5, pp. 1358–1397
  • Yuri Bakhtin, Konstantin Khanin, On global solutions of the random Hamilton-Jacobi equations and the KPZ problem https://arxiv.org/abs/1708.02134Invited article in Nonlinearity 31 (2018), pp. R93–R121
  • Yuri Bakhtin, Tobias Hurth, Sean D. Lawley, Jonathan C. Mattingly, Smooth invariant densities for random switching on the torus, https://arxiv.org/abs/1708.01390Nonlinearity 31 (2018),pp 1331–1350
  • Yuri Bakhtin, Philippe G. Lefloch, Ergodicity of spherically symmetric fluid flows outside of a Schwarzschild black hole with random boundary forcing https://arxiv.org/abs/1706.01004Stochastic PDE(2018) 6: 746-785.
  • Yuri Bakhtin, Inviscid Burgers equation with random kick forcing in noncompact setting https://projecteuclid.org/euclid.ejp/1463683782 — Electronic Journal of Probability, 21 (2016), 50pp
  • Yuri Bakhtin, Ergodic theory of the Burgers equation, 6Mb — a chapter in Probability and Statistical Physics in St. Petersburg (AMS Proceedings of Symposia in Pure Mathematics, V.91), edited by V.Sidoravicius and S.Smirnov, 2016

  • Yuri Bakhtin, Andrzej Swiech, Scaling limits for conditional diffusion exit problems, Doob's h-transform, and asymptotics for nonlinear elliptic equations http://arxiv.org/abs/1310.6023 — Transactions of American Mathematical Society, 368 (2016), 6487-6517
  • Yuri Bakhtin, Tobias Hurth, Jonathan C. Mattingly, Regularity of invariant densities for 1D-systems with random switching http://arxiv.org/abs/1406.5425 — Nonlinearity, 28 (2015), no.11, 3755– 3787
  • Yuri Bakhtin, On Gumbel limit for the length of reactive paths http://arxiv.org/abs/1312.1939 — Stochastics and Dynamics, 15 (2015), no.1
  • Yuri Bakhtin, Gumbel distribution in exit problems http://arxiv.org/abs/1307.7060— preprint only
  • Yuri Bakhtin, Eric Cator, Konstantin Khanin, Space-time stationary solutions for the Burgers equation http://arxiv.org/abs/1205.6721 — Journal of the American Mathematical Society 27 (2014), no.1, 193--238
  • Yuri Bakhtin, Burgers equation with Poisson random forcing http://arxiv.org/abs/1109.5668 — Annals of Probability 41(2013), no.4, 2961-2989
  • Yuri Bakhtin, Geometry of large random trees: SPDE approximation. In: Stochastic Geometry, Spatial Statistics and Random Fields, E.Spodarev ed., Lecture Notes in Mathematics, Vol.2068, Springer (2013), 399-420.
  • Yuri Bakhtin, Tobias Hurth, Invariant densities for dynamical systems with random switching http://arxiv.org/abs/1203.5744 — Nonlinearity 25 (2012) 2937-2952.
  • Yuri Bakhtin, Joshua Correll, A neural computation model for decision making times. — Journal of Mathematical Psychology, 56 (2012), pp. 333-340
  • Yuri Bakhtin, Decision making times in mean-field dynamic Ising model http://arxiv.org/abs/1005.4964 — Annales Henri Poincaré, Volume 13, Number 5 (2012), 1291-1303
  • Yuri Bakhtin, Leonid Bunimovich The optimal sink and the best source in a Markov chain http://arxiv.org/abs/1007.2035 — Journal of Statistical Physics (2011) Volume 143, Number 5, 943-954,
  • Yuri Bakhtin, Noisy heteroclinic networks, http://arxiv.org/abs/0712.3952 — Probab. Theory Related Fields 150 (2011), no. 1-2, 1–42
  • Sergio Almada, Yuri Bakhtin, Normal forms approach to diffusion near hyperbolic equilibria http://arxiv.org/abs/1006.3000 — Nonlinearity 24 (2011) 1883-1907
  • Sergio Almada, Yuri Bakhtin, Scaling limit for the diffusion exit problem in the Levinson case http://arxiv.org/abs/1006.2766 — Stochastic Processes and their Applications, Volume 121, Issue 1, January 2011, Pages 24–37
  • Yuri Bakhtin, SPDE Approximation for Random Trees http://arxiv.org/abs/0909.2283 — Markov Process. Related Fields 17 (2011), no. 1, 1–36,
  • Yuri Bakhtin, Small noise limit for diffusions near heteroclinic networks. — Dynamical Systems, Volume 25, Issue 3, 2010, (Special Issue: Robust Heteroclinic and Switching Dynamics)

  • Yuri Bakhtin, Carl Mueller Solutions of semilinear wave equation via stochastic cascades http://arxiv.org/abs/0911.5450 — Commun. Stoch. Anal. 4 (2010), no. 3, 425–431.
  • Yuri Bakhtin, Konstantin Khanin, Localization and Perron--Frobenius theory for directed polymers http://arxiv.org/abs/0909.2293 — Mosc. Math. J. 10 (2010), no. 4, 667–686
  • Yuri Bakhtin, Self-Similar Markov Processes on Cantor Set http://arxiv.org/abs/0810.3260 --- preprint only
  • Yuri Bakhtin, Thermodynamic limit for large random trees, http://arxiv.org/abs/0809.2974 — Random Structures Algorithms 37 (2010), no. 3, 312–331.
  • Yuri Bakhtin, Poisson limit for associated random fields http://arxiv.org/abs/0809.2971 — Teor. Veroyatn. Primen. 54 (2009), no. 4, 772--776(Russian); translation in Theory Probab. Appl. 54 (2010), no. 4, 678–681
  • Yuri Bakhtin, Christine Heitsch Large deviations for random trees and the branching of RNA secondary structures, http://arxiv.org/abs/0803.3990 --- Bull. Math. Biology, Volume 71(2009), No. 1
  • Yuri Bakhtin, Christine Heitsch Large deviations for random trees, http://arxiv.org/abs/0712.2253 --- J.Stat.Phys. (2008) 132:551-560
  • Yuri Bakhtin, Matilde Martínez A characterization of harmonic measures on laminations by hyperbolic Riemann Surfaces, math.DS/0611235 --- Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, (2008) Vol. 44, No. 6, 1078–1089
  • Yuri Bakhtin, Exit asymptotics for small diffusion about an unstable equilibrium math.PR/0701569 --- Stoch. Proc. Appl., 118 (2008), 839-851.
  • Yuri Bakhtin, Jonathan Mattingly Malliavin calculus for infinite-dimensional systems with additive noise, math.PR/0610754 --- Journal of Functional Analysis, Volume 249 (2007), Issue 2, Pages 307-353.
  • Yuri Bakhtin, Burgers equation with random boundary conditions, -- Proc. Amer. Math. Soc. 135 (2007), 2257-2262.
  • Yuri Bakhtin Existence and uniqueness of stationary solutions for 3D Navier-Stokes system with small random forcing via stochastic cascades. -- J. Stat. Phys., 2006, v.122, no.2, p.351--360.
  • Yuri Bakhtin, Lyapunov exponents for stochastic differential equations with infinite memory. Applications to stochastic Navier-Stokes system in 2D. -- Discrete Contin. Dyn. Syst. Ser. B, 2006, v.6, no.4, p.697--709
  • Yuri Bakhtin, Jonathan Mattingly Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations. -- Commun. Contemp. Math., 2005, v.7, no.5, p.553 - 582
  • Maxim Arnold, Yuri Bakhtin, Efim Dinaburg, Regularity of Solutions to Vorticity Navier-Stokes System on $\mathbf{R}^2.$ -- Comm. Math. Phys., 2005, v. 258, no. 2, p.339 - 348
  • Bakhtin Yu.Yu., Dinaburg E.I., Sinai Ya.G. On solutions of the Navier-Stokes system with infinite energy and enstrophy. In memory of A.A.Bolibrukh, -- Uspekhi Mat. Nauk, 2004, v.59, no.6, p.55-72
  • Arnold M.D., Bakhtin Yu. Yu., Dinaburg E.I. Regularity of solutions to the Navier-Stokes system on plane, -- Uspekhi Mat. Nauk, 2004, v.59, no.3(357), p.157-158
  • Bakhtin Yu.Yu. Existence and uniqueness of stationary solutions of nonlinear stochastic differential equation with memory. -- Theory Probab. Appl., 2002, v. 47, no.4, p.764-769
  • Bakhtin Yu.Yu. Limit theorems for random solutions of the Burgers equation. Ph.D.Thesis. MSU, Moscow, 2001
  • Bakhtin Yu.Yu. A functional central limit theorem for transformed solutions of the multidimensional Burgers equation with random initial data. -- Theory Probab. Appl., 2001, v. 46, no.3, p.21-44
  • Bakhtin Yu. A functional central limit theorem for parabolically rescaled random solutions of the Burgers equation. In: Abstracts of XXI Seminar on Stability Problems of Stochastic Models, Eger, 2001, p.30-31
  • Bakhtin Yu.Yu., Chervonenkis, A.Ya., Kantsel, A.V., Danilov, A.V. A method of reconstruction of a conditional distribution field. -- Avtomatika i telemechanika (Automation and Remote Control), 2000, no.12, p.75-86
  • Bakhtin Yu.Yu. A functional central limit theorem for transformed solutions of the multidimensional Burgers equation with random initial data. -- Doklady Rossiiskoi Akademii Nauk, 2000, v.372, no.6. p.5-7
  • Bakhtin Yu.Yu. A functional central limit theorem for a solution of the Burgers equation with the initial data given by an associated random measure. -- Vestnik Moskovskogo Universiteta, Ser.1, 2000, no.6, p.8-15
  • Bakhtin Yu.Yu. A functional central limit theorem for random solutions of the Burgers equation. -- Theory Probab. Appl, 1999, v.44, no.3, p.698-699
  • Bakhtin Yu. Asymptotic analysis of the Burgers equation with random initial data. -- In: Eleventh European Young Statisticians Meeting, Marly-le-Roi,1999, p.10-14
  • Bakhtin Yu.Yu. A law of the iterated logarithm for a solution of the Burgers equation with random data. -- Matematicheskie Zametki, 1998, v.64, no.6, p.812-823
  • Bakhtin Yu.Yu., Bulinski, A.V. Moment inequalities for sums of dependent multiindexed random variables. -- Fundamentalnaya i prikladnaya matematika, 1997, v.3 no.4, p.1101-1108


Grant support
  • NSF (2018-2021) DMS-1811444
  • NSF (2014-2017) DMS-1460595
  • NSF CAREER (2008-2013) DMS-0742424


Ph.D. Students
  • Hong-Bin Chen

Former Ph.D. Students
  • Donghyun Seo (Courant, 2020)
  • Liying Li (Courant, 2019)
  • Tobias Hurth (Georgia Tech, 2014)
  • Sergio Angel Almada Monter (Georgia Tech, 2011)


My guitar music and songs in Russian