On-diagonal lower estimate of heat kernel on graphs

Abstract

The purpose of this paper is to establish a new continuous-time on-diagonal lower estimate of heat kernel for large time on graphs. To achieve the goal, we first give an upper bound of heat kernel in natural graph metric, and then use this bound and the volume growth condition to show the validity of the on-diagonal lower bound.

10 pages

Cited by in corpus (2)

• The existence and nonexistence of global solutions for a semilinear heat equation on graphs
• Convergence of ground state solutions for nonlinear Schrödinger equations on graphs