5 research outputs found
Stochastic Completeness of Graphs
In this thesis, we analyze the stochastic completeness of a heat kernel on
graphs which is a function of three variables: a pair of vertices and a
continuous time, for infinite, locally finite, connected graphs. For general
graphs, a sufficient condition for stochastic completeness is given in terms of
the maximum valence on spheres about a fixed vertex. That this result is
optimal is shown by studying a particular family of trees. We also prove a
lower bound on the bottom of the spectrum for the discrete Laplacian and use
this lower bound to show that in certain cases the Laplacian has empty
essential spectrum.Comment: 72 pages, 1 figure, PhD thesi