Random Walks and Homogenization Theory

Time:Tues.15:20-16:55,Wed.9:50-11:25am, Sept.13-Dec.2,2022

Venue: Conference Room 1,Jin Chun Yuan West Bldg.;Tencent ID:355-023-8301

Speaker:Gu Chenlin


The central-limit type results are universal in many random walk models: they are known as Donsker’s theorem for the classical Zd random walk, and also hold for some random walks in random environment, even when the environment is degenerate like percolation. In their proofs, the homogenization theory, which comes from PDE, plays an important role. This course will cover the following topics:

1. Donsker’s theorem of classical random walk (2 lectures)

2. Some examples of random walks in random environments (2 lectures)

3. Homogenization theory (5 lectures)

4. Random walk on percolation cluster (3 lectures)


Basic probability and PDE


1. Armstrong, S., Kuusi, T. and Mourrat, J.C., 2019. Quantitative stochastic homogenization and large-scale regularity (Vol. 352). Springer.

2. Biskup, M., 2011. Recent progress on the random conductance model. Probability Surveys, 8, pp.294-373.

3. Dario, P. and Gu, C., 2021. Quantitative homogenization of the parabolic and elliptic Green’s functions on percolation clusters. The Annals of Probability, 49(2), pp.556-636.

4. Jikov, V.V., Kozlov, S.M. and Oleinik, O.A., 2012. Homogenization of differential operators and integral functionals. Springer Science & Business Media.

5. Lawler, G.F. and Limic, V., 2010. Random walk: a modern introduction (Vol. 123). Cambridge University Press.

DATEAugust 29, 2022
Related News
    • 0

      Topics in random matrix theory

      Description: This course will give a brief introduction to random matrix theory. Some topics we plan to cover are: Wigner semicircle law, the moment method, the resolvent method, invariant ensembles, Wigner matrices, sample covariance matrices, bulk universality, edge universality, rigidity of eigenvalues, Dyson Brownian motion, Tracy-Widom law, and free probability.Prerequisite:Probability, S...

    • 1

      Fundmental theory of quantum channels (II)

      IntroductionThis course will focus on a formal presentation of definitions and theorems on quantum channels in quantum information theory.Numerous mathematical proofs of these theorems will be showed.Lecturer IntroMeng Cao received the PhD degree from the Department of Mathematical Sciences, Tsinghua University, in Aug. 2020. From Sep. 2020 to Nov. 2022, he worked as a postdoctoral researcher i...