# A graph counterexample to Davies’ conjecture

### Gady Kozma

Weizmann Institute of Science, Rehovot, Israel

## Abstract

There exists a graph with two vertices $x$ and $y$ such that the ratio of the heat kernels $p(x,x;t)/p(y,y;t)$ does not converge as $t\to\infty$.

## Cite this article

Gady Kozma, A graph counterexample to Davies’ conjecture. Rev. Mat. Iberoam. 30 (2014), no. 1, pp. 1–12

DOI 10.4171/RMI/766