Yuri Bakhtin

Associate Professor

241 Skiles Building
School of Mathematics
Georgia Institute of Technology
Atlanta, Georgia 30332

Email:

Research interests: random dynamics, probabilistic models of mathematical physics

Teaching:

Spring 2013: Math 7245 Stochastic Processes and Stochastic Calculus II and Math 3215 Introduction to Probability and Statistics, (the courses are maintained via T-Square)

Fall 2012: Math 7244 Stochastic Processes and Stochastic Calculus (the course is maintained via T-Square)

Fall 2011: Math 7244 Stochastic Processes and Stochastic Calculus (the course is maintained via T-Square)

Spring 2011: Math 3215 Introduction to Probability and Statistics (the course is maintained via T-Square)

Fall 2010: Math 6235 Stochastic Processes in Finance II (the course is maintained via T-Square)

Spring 2010: Math 6221 Advanced Classical Probability Theory (the course is maintained via T-Square)

Fall 2009: Math 1502 Claculus II (the course is maintained via T-Square)

Spring 2009: Math 3215 Introduction to Probability and Statistics, Math 4221 Stochastic Processes I

Fall 2008: Math 7245 Stochastic Processes and Stochastic Calculus II

Spring 2008: Math 7244 Stochastic Processes and Stochastic Calculus I, Math 4221 Stochastic Processes I

Fall 2007: Math 7245 Stochastic Processes and Stochastic Calculus II

Spring 2007: Math 7244 Stochastic Processes and Stochastic Calculus I

Fall 2006: Math 6242 Probability II

AWARDS/GRANTS

• NSF CAREER (2008-2013) DMS-0742424

• Yuri Bakhtin, Ergodic theory of the Burgers equation — a chapter in a forthcoming volume of lecture notes for Summer School on Probability and Statistical Physics in St.Petersburg, 2012, edited by V.Sidoravicius and S.Smirnov.
• Yuri Bakhtin, Eric Cator, Konstantin Khanin, Space-time stationary solutions for the Burgers equation http://arxiv.org/abs/1205.6721 — accepted at JAMS.
• Yuri Bakhtin, Burgers equation with Poisson random forcing http://arxiv.org/abs/1109.5668 — accepted at Annals of Probability
• Sergio Almada, Yuri Bakhtin, Small noise estimates of the quadratic covariation between non-smooth transformations of Brownian motion http://arxiv.org/abs/1108.3602 — Submitted
• 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 -- 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