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4 papers · 2 filters
Some remarks on the elliptic Harnack inequality
Martin T. Barlow
This note gives three short results concerning the elliptic Harnack inequality (EHI), in the context of random walks on graphs. The first is that the EHI implies polynomial growth…
Extra heads and invariant allocations
Alexander E. Holroyd, Yuval Peres
Let Πbe an ergodic simple point process on R^d and let Π^* be its Palm version. Thorisson [Ann. Probab. 24 (1996) 2057-2064] proved that there exists a shift coupling of Πand Π^*;…
Integrals, Partitions, and Cellular Automata
Alexander E. Holroyd, Thomas M. Liggett, Dan Romik
We prove that where is the decreasing function that satisfies , for . When is an integer and $b=…
Random walks on supercritical percolation clusters
Martin T. Barlow
We obtain Gaussian upper and lower bounds on the transition density q_t(x,y) of the continuous time simple random walk on a supercritical percolation cluster C_{\infty} in the Eucl…