Technical University of Berlin

Wed 18 Oct 2017, 3:00pm
Probability Seminar
ESB 2012

Harnack inequality for degenerate balanced random walks

ESB 2012
Wed 18 Oct 2017, 3:00pm4:00pm
Abstract
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.
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University of Alberta at Edmonton

Wed 1 Nov 2017, 3:00pm
Probability Seminar
ESB 2012

FeynmanKac formula for the stochastic heat equation driven by general Gaussian noises

ESB 2012
Wed 1 Nov 2017, 3:00pm4:00pm
Abstract
In this talk I will present some results on stochastic heat equations driven by a Gaussian noises. I will focus on FeynmanKac representation of the solution and the moments of the solution. Both lower and upper bounds for the L^p moments of the solution are obtained which is relevant to the socalled intermittency. The Driving Gaussian noises include fractional Brownian fields of Hurst parameters greater or smaller than 1/2.
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