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)
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*), submitted, 2023. (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)