Abstract:

Motivated by the tensionless KPZ equation (a model of stochastic growth), we consider quantitative large-time averages for Hamilton–Jacobi equations in a dynamic random environment that is stationary ergodic and has finite-range dependence in time. In this talk, we establish, up to slowly varying factors, convergence rates with exponent 1/2 for the large-time averages of both the solutions and the associated metric problem toward their ergodic limits. Our proof introduces a new almost-Lipschitz regularity theory for the metric problem, which is of independent interest. Joint work with Wenjia Jing (Tsinghua), Hung V. Tran (Wisconsin), and Yuming Zhang (Auburn).

Bio:

Xiaoqin Guo is an associate professor of mathematics in the University of Cincinnati. He received PhD in mathematics from the University of Minnesota in 2012, and has been worked in Technical University of Munich and in University of Wisconsin at Madison. His research field is probability theory and recently  interactions with PDEs. He has published about 20 papers in math journals including in Annals of Probability, PTRF, Ann. Inst. Henri Poincaré Probab. Stat. and Calculus of Variations and PDEs.