A Percolating Hard Sphere Model (2006)
Cotar, Codina, Holroyd, Alexander E., Revelle, David
Given a homogeneous Poisson point process in R^d, Haggstrom and Meester asked whether it is possible to place spheres (of differing radii) centred at the points, in a translation-invariant way, so...
Mixing Times for Random Walks on Finite Lamplighter Groups (2004)
Peres, Yuval; University Of California; Peres@stat.berkeley.edu, Revelle, David; University Of California; Revelle@stat.berkeley.edu
Given a finite graph G, a vertex of the lamplighter graph consists of a zero-one labeling of the vertices of G, and a marked vertex of G. For transitive graphs G, we show that, up to constants, the...
Scaling limits of the uniform spanning tree and loop-erased random walk on finite graphs (2004)
Let x and y be chosen uniformly in a graph G. We find the limiting distribution of the length of a loop-erased random walk from x to y on a large class of graphs that include the discrete torus in...
Mixing times for random walks on finite lamplighter groups (2004)
Given a finite graph G, a vertex of the lamplighter graph consists of a zero-one labeling of the vertices of G, and a marked vertex of G. For transitive graphs G, we show that, up to constants, the...
Heat Kernel Asymptotics on the Lamplighter Group (2003)
Revelle, David; UC Berkeley; Revelle@stat.berkeley.edu
We show that, for one generating set, the on-diagonal decay of the heat kernel on the lamplighter group is asymptotic to $c_1 n^{1/6}exp[-c_2 n^{1/3}]$. We also make off-diagonal estimates which show...
Heat Kernel Asymptotics on the Lamplighter Group (2003)
Revelle, David; UC Berkeley; Revelle@stat.berkeley.edu
We show that, for one generating set, the on-diagonal decay of the heat kernel on the lamplighter group is asymptotic to $c_1 n^{1/6}exp[-c_2 n^{1/3}]$. We also make off-diagonal estimates which show...
Instability of set recurrence and Green's function on groups with the Liouville property (2003)
Benjamini, Itai, Revelle, David
Let $\mu$ and $\nu$ be probability measures on a group \Gamma and let G_\mu and G_\nu denote Green's function with respect to \mu and \nu . The group \Gamma is said to admit instability of Green's...
Rate of escape of random walks on wreath products and related groups (2003)
This article examines the rate of escape for a random walk on $G\wr \Z$ and proves laws of the iterated logarithm for both the inner and outer radius of escape. The class of G for which these results...
Time to stationary for random walks on random graphs / (1996)
Thesis (A.B., Honors in Mathematics)--Harvard University, 1996.