Professor

https://mfeapp.baruch.cuny.edu/math/elenak/”> Baruch College and the Department of Mathematics, Box B6-230

Baruch College

New York, NY 10010

USA

*Office hours:* by appointment (on Scholar Incentive leave for the academic year 2014-2015)

*Current research interests:*

- Random walks and diffusions in random media

* Education:*

*Undergraduate:*

- Diploma in Mathematics (with Honors), 1989, Moscow State University, Adviser: A.S. Kalashnikov. Diploma paper: “On unbounded solutions of quasi-linear degenerate parabolic equations”.

*Graduate:*

- Candidate of Science in Physics and Mathematics, 1995, Moscow State University, Department of Mathematics and Mechanics, Adviser: A.S. Kalashnikov. Dissertation: “Cauchy problem in classes of growing functions for equations of fast diffusion type”.
- Ph.D. in Mathematics, 1999, Courant Institute, New York University, Mathematics,

Adviser: S.R.S. Varadhan. Dissertation: “Behavior of relative entropy in the hydrodynamic scaling limit”. PDF

*Some papers and preprints:*

Dolgopyat, D. Kosygina, E., *Excursions and occupation times of critical excited random walks, *arxiv:1410.7090

Kosygina, E., Zerner, M.P.W., *Excursions of excited random walks on integers, *Electronic Journal of Probability 19 (2014), article 25, 1-25

Kosygina, E., *Crossing speeds of random walks among “sparse” or “spiky” Bernoulli potentials on integers, *Journal of Statistical Physics, 152 (2013), no. 2, 213-236; arXiv:1212.4447

Kosygina, E., Zerner, M. P. W., *Excited random walks: results, methods, open problems.* Bulletin of the Institute of Mathematics. Academia Sinica (New Series) 8 (2013), no. 1, 105-157; Published version; arXiv:1204.1895

Dolgopyat, D., Kosygina, E.,* Scaling limits of recurrent excited random walks on integers. * Electronic Communications in Probability 17 (2012), article 35, 1-14.

Kosygina, E., Mountford, T., *Crossing velocities for an annealed random walk in a random potential.* Stochastic Processes and their Applications 122 (2012), no. 1, 277–304. arXiv:1103.0515v1.

Kosygina, E., Mountford, T., *Limit laws of transient excited random walks on integers.* Annales de l’Institut Henri Poincare, Probabilites et Statistiques, 47 (2011), no. 2, 575-600. arXiv:0908.4356v2.

Kosygina, E., Mountford, T. S., Zerner, M.P.W., *Lyapunov exponents of Green’s functions for random potentials tending to zero.* Probability Theory and Related Fields, 150 (2011), no. 1-2, 43-59. arXiv:0903.4928v2.

Kosygina, E., Zerner, M.P.W., *Positively and negatively excited random walks on integers, with branching processes.* Electronic Journal of Probability, 13 (2008), paper 64, 1952-1979.

Kosygina, E., Varadhan S.R.S., *Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium.* Communications on Pure and Applied Mathematics, 61 (2008), no. 6, 816-847. PDF

Kosygina, E., *Homogenization of stochastic Hamilton-Jacobi equations: brief review of methods and applications.* Stochastic Analysis and Partial Differential Equations, Series of Contemporary Mathematics 429 (2007), American Mathematical Society, 189-204. PDF

Kosygina, E., Rezakhanlou, F., and Varadhan, S.R.S., *Stochastic homogenization of Hamilton-Jacobi-Bellman Equations.* Communications on Pure and Applied Mathematics, 59 (2006), no. 10, 1489-1521.PDF

Kosygina, E., *Brownian flow on a finite interval with jump boundary conditions.* Discrete and Continuous Dynamical Systems, Series B, 6 (2006), no. 4, 867-880. PDF

Kosygina, E., *On the Cauchy problem for the generalized porous medium equation.* Communications in Partial Differential Equations, 26 (2001), 841-858. PDF

Kosygina, E., *The behavior of the specific entropy in the hydrodynamic scaling limit.* The Annals of Probability, 29 (2001), no. 3, 1086-1110. PDF

Kosygina, E., *The behavior of the specific entropy in the hydrodynamic scaling limit for Ginzburg-Landau model.* Markov Processes and Related Fields, 7 (2001), no. 3, 383-417. PDF

#### Current Grants:

- Collaboration Grant for Mathematicians, Simons Foundation, #209493, July 1, 2011 – August 31, 2016
- Simons Fellowship in Mathematics, 2014-2015

#### Links to local probability seminars:

CUNY Probability Seminar, Tuesdays, 4:15-5:15 p.m., Rm 5417

Courant Institute Probability and Mathematical Physics Seminar, Fridays, 11 a.m.-12 p.m., Rm 512

Columbia University Probability Seminar, Fridays, 12-1 p.m., Rm 520

`Last updated: 11/2014`