Time: 14:00-15:30, Friday, January 30 2026
Venue: E14-212
Speaker: Qiang Xu, Lanzhou University
Biography：Qiang Xu, born on March 6, 1987, in Shanxi Province, is an Associate Professor at the School of Mathematics and Statistics, Lanzhou University. He holds a Ph.D. in Fundamental Mathematics from Lanzhou University (2016) and participated in a Joint Ph.D. Program at the University of Kentucky (2013-2015). His advisors are Zhongwei Shen and Peihao Zhao.
With postdoctoral position at Peking University (2016-2018) and Max Planck Institute for Mathematics in the Sciences (2018-2020), he has focused his research on quantitative stochastic homogenization theory. He has published papers in journals like Math. Ann., Found. Comput. Math., SIAM J. Math. Anal., Calc. Var. Partial Differential Equations, J. Differential Equations, etc.
Title: Bias in the Representative Volume Element method: Periodize the Ensemble Instead of Its Realizations
Abstract: We study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior of a stationary random medium. The latter is described by a coefficient field generated from a given ensemble and the corresponding linear elliptic operator of second order. In line with the theory of homogenization, the method proceeds by computing correctors. To be numerically tractable, this computation has to be done on a finite domain: the so-called RVE, i.e., a large box with the lateral size L and periodic boundary conditions. The main message of this talk is that systematic error (i.e., the bias) can be expressed as O(L^d). We carry out the rigorous analysis in the convenient setting of the ensembles of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for stochastic estimates of correctors. This is a joint work with Nicolas Clozeau, Marc Josien, and Felix Otto.
