分野別セミナー

Abstract: We will consider the following two models and establish quenched invariance principles; 1. Simple random walks on the infinite clusters for super-critical percolations on half and quarter planes in d-dimensional Euclidean spaces. 2. Uniform elliptic divergence forms with random stationary coefficients on cones in Euclidean spaces. Note that because of the lack of translation invariance we cannot apply the method of the 'corrector'. Instead we make full use of the heat kernel estimates and Dirichlet form techniques to resolve the problem. This is a joint work with Z.Q. Chen (Seattle) and D.A. Croydon (Warwick).