Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks
Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks
The difference Laplacian on a square lattice in Rn has been studied by many authors.In this paper an analogous difference operator is studied for an arbitrary graph.It is shown that many properties of the Laplacian in the continuous setting (e.g. the maximum principle, the Harnack inequality, and Cheeger's bound for …