The present book deals with the spectral geometry of infinite graphs. This topic involves the
interplay of three different subjects: geometry, the spectral theory of Laplacians and the heat …

In order to become worldly things, that is, deeds and facts and events and patterns of
thoughts or ideas,[action, speech, and thought] must first be seen, heard, and remembered …

Discrete time random walks on a finite set naturally translate via a one-to-one
correspondence to discrete Laplace operators. Typically, Ollivier curvature has been …

Abstract Let G=(V, E) G=(V, E) be a finite or locally finite connected weighted graph, Δ Δ be
the usual graph Laplacian. Using heat kernel estimates, we prove the existence and …

We study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on
weighted graphs. We first show that, for locally finite graphs and a certain family of metrics …

We prove pointwise gradient bounds for heat semigroups associated to general (possibly
unbounded) Laplacians on infinite graphs satisfying the curvature dimension condition CD …

Studying the heat semigroup, we prove Li–Yau-type estimates for bounded and positive
solutions of the heat equation on graphs. These are proved under the assumption of the …

For a given subcritical discrete Schrödinger operator H on a weighted infinite graph X, we
construct a Hardy-weight w which is optimal in the following sense. The operator H− λ w is …

We investigate quantum graphs with infinitely many vertices and edges without the common
restriction on the geometry of the underlying metric graph that there is a positive lower …

We study solutions of the generalized porous medium equation on infinite graphs. For
nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild …