Yuri Bakhtin

Assistant Professor

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

Email:

Office phone: (404)-894-9235

Office hours: Tuesday, Thursday 9:30-10:30AM

Research interests: random dynamics, probabilistic models of mathematical physics

Teaching:

Fall 2009: Math 1502 (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

• Bakhtin Yu., SPDE Approximation for Random Trees http://arxiv.org/abs/0909.2283 --- submitted
• Bakhtin Yu., Khanin K. Localization and Perron--Frobenius theory for directed polymershttp://arxiv.org/abs/0909.2293 --- submitted
• Bakhtin Yu., Self-Similar Markov Processes on Cantor Sethttp://arxiv.org/abs/0810.3260 --- submitted
• Bakhtin Yu., Thermodynamic limit for large random trees, http://arxiv.org/abs/0809.2974 --- accepted at Random Structures and Algorithms.
• Bakhtin Yu., Poisson limit for associated random fields http://arxiv.org/abs/0809.2971 --- accepted at Theory of Probability and its Applications
• Bakhtin Yu., Noisy heteroclinic networks, http://arxiv.org/abs/0712.3952 --- submitted
• Bakhtin Yu., Heitsch C.E. 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
• Bakhtin Yu., Heitsch C.E. Large deviations for random trees, http://arxiv.org/abs/0712.2253 --- J.Stat.Phys. (2008) 132:551-560
• Bakhtin Yu., Martínez M. 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
• Bakhtin Yu. Exit asymptotics for small diffusion about an unstable equilibrium math.PR/0701569 --- Stoch. Proc. Appl., 118 (2008), 839-851.
• Bakhtin Yu., Mattingly J. C. Malliavin calculus for infinite-dimensional systems with additive noise, math.PR/0610754 --- Journal of Functional Analysis, Volume 249 (2007), Issue 2, Pages 307-353.
• Bakhtin Yu. Burgers equation with random boundary conditions, -- Proc. Amer. Math. Soc. 135 (2007), 2257-2262.
• Bakhtin Yu. 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.
• Bakhtin Yu. 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
• Bakhtin Yu., Mattingly J.C. Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations. -- Commun. Contemp. Math., 2005, v.7, no.5, p.553 - 582
• Arnold M.D., Bakhtin Yu. Yu., Dinaburg E.I. 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

SLIDES FROM RECENT PRESENTATIONS IN PDF

• Burgers equation with random boundary conditions --- SPA'07 at Urbana-Champaign, August 2007.