Department of Mathematics

Baruch College and the CUNY Graduate Center (on leave for 2024-2025)

**Contact Information:***Email:* elena.kosygina “at” baruch.cuny.edu*Phone:* +1 (646) 312-4167

**Mailing address:**

One Bernard Baruch Way

Department of Mathematics, Box B6-230

Baruch College

New York, NY 10010

USA

**Current research interests:**

- Random walks and diffusions in random media
- Stochastic homogenization of Hamilton-Jacobi equations

** 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“.

**Graduate students:**

- Omar Chakhtoun (CUNY Graduate Center, PhD, February 2019). Dissertation:
.*One-dimensional excited random walk with unboundedly many excitations per site*

**Papers and preprints:**

Kosygina, E., Yilmaz, A., Homogenization of nonconvex viscous Hamilton-Jacobi equations in stationary ergodic media in one dimension; 20 pages; arXiv:2403.15963

Kosygina, E., Yilmaz, A., Loss of quasiconvexity in the periodic homogenization of viscous Hamilton-Jacobi equations; 24 pages; arXiv:2309.09343

Davini, A., Kosygina, E., Yilmaz, A., Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations in one space dimension; 31 pages; accepted for publication by Communications in Partial Differential Equations; arXiv:2303.06415

Kosygina, E., Mountford, T., Peterson, J., *Convergence and non-convergence of of scaled self-interacting random walks to Brownian motion perturbed at extrema*; Annals of Probability, 51 (2023), no. 5, 1684-1728; published version; arxiv:2208.02589

Kosygina, E., Mountford, T., Peterson, J., *Convergence of random walks on Markovian cookie stacks to Brownian motion perturbed at extrema; Probability Theory and Related Fields*, 182 (2022), no. 1-2, 189-275; published version; arXiv:2008.06766

Davini, A., Kosygina, E., *Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension; Journal of DIfferential Equations, 333 (2022), 231-267; published version; *arXiv:2002.02263

Kosygina, E., Yilmaz, A., Zeitouni, O., *Homogenization of a class of one-dimensional non-convex viscous Hamilton-Jacobi equations with random potential; Communications in Partial Differential Equations,* 45 (2020), no. 1, 32–56; published version; arXiv:1710.03087

Davini, A., Kosygina, E., *Homogenization of viscous and non-viscous HJ equations: a remark and an application; Calculus of Variations and Partial Differential Equations*, 56 (2017), paper 95, 21 pages; arXiv:1608.01893v2; published version (print/download is not allowed; misprints: missing commas in A(x/ε,ω) between x/ε and ω in 3 places)

Kosygina, E., Zerner, M. P. W., *A zero-one law for recurrence and transience of frog processes*; Probability Theory and Related Fields, 168 (2017), no. 1-2, 317–346; published version*; arXiv:1508.01953 (*print/download is not allowed)

Kosygina, E., Peterson, J., *Excited random walks with Markovian cookie stacks*; Annales de L’Institute Henri Poincaré, Probabilités et Statistiques, 53 (2017), no. 3, 1458-1497; arXiv:1504.06280

Kosygina, E., Peterson, J., *Functional Limit laws for recurrent excited random walks with Markovian cookie stacks; *Electronic Journal of Probability*,* 21 (2016), paper no. 70, 24 pp.

Dolgopyat, D., Kosygina, E., *Excursions and occupation times of critical excited random walks*; ALEA Lat. Am. J. Probab. Math. Stat.12 (2015), no. 1, 427–450. 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., 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

- PSC CUNY Traditional B Award 64512-00 52, July 1, 2021 – June 30, 2022
- Collaboration Grant for Mathematicians, Simons Foundation, September 1, 2017 – August 31, 2022 (no cost extension until 2024)
- Simons Fellow in Mathematics, Simons Foundation, 2014-2015
- Collaboration Grant for Mathematicians, Simons Foundation, July 1, 2011 – August 31, 2016 (no cost extension until August 31, 2017)

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

Courant Institute Probability and Mathematical Physics Seminar

Columbia University Probability Seminar