Research

"In fact, all epistemological value of the theory of probability is based on this: that large-scale random phenomena in their collective action create strict, nonrandom regularity."

---Gnedenko and Kolmogorov, Limit Distributions for Sums of Independent Random Variables, P.1

Note: A conjecture related to paper 4: PDF.

Papers

1. Policy iteration for nonconvex viscous Hamilton--Jacobi equations (with H.V. Tran, Y.P. Zhang)

arXiv2503.02159

1. On the rate of convergence of the martingale central limit theorem in Wasserstein distances

arXiv2407.16980

1. Optimal convergence rates in stochastic homogenization in a balanced random environment (with H.V. Tran)

arXiv2301.01267

1. Characterizations of diffusion matrices in homogenization of elliptic equations in nondivergence-form (with T. Sprekeler, H.V. Tran)

Cal. Var. PDE. 64, 1 (2025).

1. Stochastic integrability of heat-kernel bounds for random walks in a balanced random environment (with H.V. Tran)

Electron. J. Probab. 29 (2024), no. 194, 1-31 .

1. Quantitative homogenization in a balanced random environment (with J. Peterson, H. V. Tran)

Electron. J. Probab. 27 (2022), no. 132, 1–31.

1. An elliptic Harnack inequality for difference equations with random balanced coefficients (with N. Berger, M. Cohen, J.-D. Deuschel)

Ann. Probab. 2022, Vol.50(3), 835-873

1. Quenched local central limit theorem for random walks in a time-dependent balanced random environment (with J.-D. Deuschel)

Probab. Theory Relat. Fields (2022) 182:111–156

1. Remarks on optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form (with H. V. Tran, Y. Yu)

Partial Differ. Equ. Appl. 1, 15 (2020).

1. Invariance principles for random walk in elliptic and non-elliptic balanced random environment (with N. Berger, J.D. Deuschel, A. Ramirez) In preparation
2. Berry-Esseen estimates for regenerative processes under weak moment assumptions (with J. Peterson)

Stochastic Process. Appl. 129 (4):1379 - 1412, 2019.