Harmonic functions and random walks on infinite planar graphs
Speaker: Wai Yeung Lam
Time: 15:20 - 16:55, every Monday,Wednesday, 3/14/2022 - 6/8/2022
Zoom ID: 638 227 8222，Password：BIMSA
From the view point of potential theory, infinite graphs form a discrete model of noncompact Riemannian manifolds. For a discrete Laplacian on a network, the corresponding discrete Poisson equation is related to Kirchhoff's electric circuit laws. On the other hand, there is an interplay between infinite networks and the theory of Markov chains. In this course, we introduce basic results on infinite networks, such as extremal length. We will discuss its connections to circle packings.
Soardi, Paolo M. Potential theory on infinite networks. Lecture Notes in Mathematics, 1590. Springer-Verlag, Berlin, 1994.