Revista Matemática Iberoamericana

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Volume 30, Issue 1, 2014, pp. 1–12
DOI: 10.4171/RMI/766

Published online: 2014-03-23

A graph counterexample to Davies’ conjecture

Gady Kozma[1]

(1) Weizmann Institute of Science, Rehovot, Israel

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 $t\to\infty$.

Keywords: Strong ratio limit, rough isometry, quasi-isometry, jungle gym

Kozma Gady: A graph counterexample to Davies’ conjecture. Rev. Mat. Iberoam. 30 (2014), 1-12. doi: 10.4171/RMI/766