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, Hong-Bin Chen, Atypical exit events near a repelling equilibrium https://arxiv.org/abs/1911.06437 29pp
  • Yuri Bakhtin, Hong-Bin Chen, Long exit times near a repelling equilibrium https://arxiv.org/abs/1908.11840 29pp
  • Yuri Bakhtin, Donghyun Seo, Localization of directed polymers in continuous space https://arxiv.org/abs/1905.00930 56pp
  • Yuri Bakhtin, Liying Li, Strongly mixing smooth planar vector field without asymptotic directions https://arxiv.org/abs/1903.02733 22pp
  • Yuri Bakhtin, Zsolt Pajor-Gyulai, Tails of exit times from unstable equilibria on the line https://arxiv.org/abs/1810.05341 17pp
  • Yuri Bakhtin, Liying Li, Weakly mixing smooth planar vector field without asymptotic directions https://arxiv.org/abs/1808.05544 10pp
  • Yuri Bakhtin, Alexisz Gaál, Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium https://arxiv.org/abs/1901.05513 12pp, accepted at Stochastics and Dynamics
  • 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
  • Donghyun Seo
  • Hong-Bin Chen

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