Probability Seminar: Jean-Dominique Deuschel

  • Date: 10/18/2017
  • Time: 15:00
Lecturer(s):
Jean-Dominique Deuschel, Technical University of Berlin
Location: 

University of British Columbia

Topic: 

Harnack inequality for degenerate balanced random walks

Description: 

We consider an i.i.d. balanced environment omega(x,e)=omega(x,-e), genuinely d dimensional on the lattice and show that there exist a positive constant C and a random radius R(omega) with streched exponential tail such that every non negative omega harmonic function u on the ball B_{2r} of radius 2r>R(omega), we have max_{B_r} u <= C min_{B_r} u. Our proof relies on a quantitative quenched invariance principle for the corresponding random walk in balanced random environment and a careful analysis of the directed percolation cluster. This result extends Martins Barlow's Harnack's inequality for i.i.d. bond percolation to the directed case. This is joint work with N. Berger, M. Cohen, and X. Guo.

Other Information: 

Location: ESB 2012