My interest research lies mainly in the field of Probability and Stochastic Differential Equations. I am currently working on Lyapunov constructions for SDEs to obtain ergodicity and mixing. 

Publications/Preprints:

(* denotes undergraduate students)

20. Exponential mixing for the stochastic Kuramoto-Sivashinsky equation on the 1D torus (with Peng Gao), submitted, 2025. (arXiv) 

19. Existence and higher regularity of statistically steady states for the stochastic Coleman-Gurtin equation (with Nathan Glatt-Holtz and Vincent Martinez), Evol. Equ. Control Theory 14 (6): 1367-1411, 2025. (arXiv)

18. Exponential mixing in a hydrodynamic pilot-wave theory with singular potentials (with Anand Oza), submitted, 2024. (arXiv) 

17. Trend to equilibrium and Newtonian limit for the relativistic Langevin equation with singular potentials (with Manh Hong Duong), submitted, 2024. (arXiv)

16. The inviscid limit for long time statistics of the one-dimensional stochastic Ginzburg-Landau equation, submitted, 2024. (arXiv) 

15.  Geometric ergodicity of a stochastic Hamiltonian system (with Lekun Wang*), J. Math. Anal. Appl. 552 (2), 2025. (arXiv)

14. Asymptotic analysis for the generalized Langevin equation with singular potentials (with Manh Hong Duong), J. Nonlinear Sci. 34 (4), 1-63, 2024. (arXiv)

13. The short memory limit for long time statistics in a stochastic Coleman-Gurtin model of heat conduction (with Nathan Glatt-Holtz and Vincent Martinez), submitted, 2022. (arXiv)

12. The invariant measure of a walking droplet in hydrodynamic pilot-wave theory (with Anand Oza), Nonlinearity 37 (9), 1-37, 2024. (arXiv)

11. Polynomial mixing of a stochastic wave equation with dissipative damping, Appl. Math. Optim. 89 (1), 1-31, 2024. (arXiv)

10. The small mass limit for long time statistics of a stochastic nonlinear damped wave equation, J. Differ. Equ. 371, 481–548, 2023. (arXiv)

9. Ergodicity of a nonlinear stochastic reaction-diffusion equation with memory, Stoch. Process. Their Appl. 155,  147-179, 2023. (arXiv)

8. Gibbsian dynamics and the generalized Langevin equation (with David Herzog and Jonathan Mattingly), Electron. J. Probab. 28, 1-29, 2023. (arXiv)

7. Stability and invariant measure asymptotics in a model for heavy particles in rough turbulent flows (with David Herzog), Commun. Math. Phys. 405 (2), 2024. (arXiv)

6. The generalized Langevin equation in harmonic potentials: anomalous diffusion and equipartition of energy (with Gustavo Didier), Commun. Math. Phys. 393 (2), 909-954,  2022. (arXiv)

5. On the Holder regularity of a linear stochastic partial-integro-differential equation with memory (with Scott McKinley), J. Fourier Anal. Appl. 28 (2), 1-31, 2022. (arXiv)

4. Asymptotic analysis of mean-squared displacement under fractional memory kernels (with Gustavo Didier), SIAM J. Math. Anal. 52 (4), 3818-3842, 2020 . (arXiv)

3. The generalized Langevin equation with power-law memory in a nonlinear potential well (with Nathan Glatt-Holtz, David Herzog and Scott McKinley), Nonlinearity 33 (6), 2820-2852, 2020 . (arXiv)

2. The small-mass limit and white-noise limit of an infinite dimensional generalized Langevin equation. J. Stat. Phys. 173 (2), 411-437, 2018. (arXiv)

1. Anomalous diffusion and the generalized Langevin equation (with Scott McKinley). SIAM J. Math. Anal. 50 (5), 5119-5160, 2018. (arXiv)