Yuri Bakhtin

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

Research interests: random dynamics, probabilistic models of mathematical physics

Email:
A link for students wishing to email me

Office: CI/WWH 729

Bibliography

Yuri Bakhtin, Konstantin Khanin, András Mészáros, Jeremy Voltz, Last passage percolation in a product-type random environment https://arxiv.org/abs/2310.08379 36pp

Yuri Bakhtin, Douglas Dow, Differentiability of the effective Lagrangian for Hamilton-Jacobi-Bellman equations in dynamic random environments https://arxiv.org/abs/2305.17276 27pp

Yuri Bakhtin, Douglas Dow, Differentiability of the shape function for directed polymers in continuous space https://arxiv.org/abs/2303.04224 28pp

Yuri Bakhtin, Hong-Bin Chen, Zsolt Pajor-Gyulai, Rare transitions in noisy heteroclinic networks, https://arxiv.org/abs/2205.00326, 141pp accepted at the Memoirs of the American Mathematical Society

Yuri Bakhtin, Douglas Dow, Joint localization of directed polymers, https://arxiv.org/abs/2211.05916 Electronic Journal of Probability, 28: 1-43 (2023)

Yuri Bakhtin, Liying Li, Strongly mixing smooth planar vector field without asymptotic directions https://arxiv.org/abs/1903.02733 Nonlinearity (2023) 36 1789

Yuri Bakhtin, Hong-Bin Chen, Dynamic polymers: invariant measures and ordering by noise https://arxiv.org/abs/2101.05653, Probability Theory and Related Fields, 183, pp. 167–227 (2022)

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 SIAM J. Appl. Dyn. Syst., 20(4), 1917–1958 (2021)

Yuri Bakhtin, Hong-Bin Chen, Atypical exit events near a repelling equilibrium https://arxiv.org/abs/1911.06437 Ann. Probab. 49(3): 1257-1285 (May 2021).

Yuri Bakhtin, Hong-Bin Chen, Long exit times near a repelling equilibrium https://arxiv.org/abs/1908.11840 Ann. Appl. Probab. 31(2): 594-624 (April 2021)

Yuri Bakhtin, Mikhail I. Katsnelson, Yuri I. Wolf, Eugene V. Koonin Evolution in the weak-mutation limit: Stasis periods punctuated by fast transitions between saddle points on the fitness landscape PNAS, January 26, 2021 118 (4) e2015665118

Yuri Bakhtin, Donghyun Seo, Localization of directed polymers in continuous space https://arxiv.org/abs/1905.00930 Electron. J. Probab. 25(none): 1-56 (2020).

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/1607.04864 — Comm. 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/1708.02134 — Invited 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/1708.01390 — Nonlinearity 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/1706.01004 — Stochastic 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

Teaching

Spring 2024: Essentials of Probability
Fall 2023: Honors ODEs (the course webpage is on Brightspace)
Spring 2023 (second half of the semester): Advanced topics in Probability. Random perturbations of dynamical systems.
Spring 2023: Applied Stoschastic Analysis (the course webpage is on Brightspace)
Fall 2022: Honors ODEs (the course webpage is on Brightspace)
Spring 2022: Probability II
Spring 2022 (second half of the semester): Advanced topics in Probability. Directed Polymers.
Fall 2021: Theory of Probability
Spring 2020: Probability: Limit Theorems II
Fall 2019: Honors III (Introduction to Stochastic Processes), via NYU Classes
Spring 2019:
- Probability: Limit Theorems II.
- Ergodicity for stochastic PDEs (joint with Pierre Germain and Jalal Shatah)
Spring 2018: Probability: Limit Theorems II
Fall 2017: Basic Probability
Spring 2017: Probability and Statistics
Fall 2016: Basic Probability
Fall 2015: Topics course on Ergodic theory of Markov processes.
Spring 2015: Probability: Limit Theorems II
Fall 2014: Probability: Limit Theorems I

Awards

Fellow of the Institute of Mathematical Statistics (2021)
NSF award DMS-2243505 (2023-2026)
NSF award DMS-1811444 (2018-2022)
NSF award DMS-1460595 (2014-2017)
NSF CAREER award DMS-0742424 (2008-2013)

Ph.D. Students

Douglas Dow

Former Ph.D. Students

Hong-Bin Chen (Courant, 2022)
Donghyun Seo (Courant, 2020)
Liying Li (Courant, 2019)
Tobias Hurth (Georgia Tech, 2014)
Sergio Angel Almada Monter (Georgia Tech, 2011)

Former Postdocs

Alexander Dunlap
Zsolt Pajor-Gyulai

Editorial Work

Stochastics and Dynamics
Former editorial board member of SIMA and SIADS.

Personal

My guitar music and songs in Russian

CV(pdf)