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Publications Influence

Choosing a Spanning Tree for the Integer Lattice Uniformly

- R. Pemantle
- Mathematics
- 1 October 1991

Consider the nearest neighbor graph for the integer lattice Zd in d dimensions. For a large finite piece of it, consider choosing a spanning tree for that piece uniformly among all possible subgraphs… Expand

240 57- PDF

Conceptual proofs of L log L criteria for mean behavior of branching processes

- R. Lyons, R. Pemantle, Y. Peres
- Mathematics
- 1 July 1995

The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and subcritical cases,… Expand

385 42- PDF

Local Characteristics, Entropy and Limit Theorems for Spanning Trees and Domino Tilings Via Transfer-Impedances

- R. Burton, R. Pemantle
- Mathematics
- 1 July 1993

Let G be a finite graph or an infinite graph on which Z^d acts with finite fundamental domain. If G is finite, let T be a random spanning tree chosen uniformly from all spanning trees of G; if G is… Expand

225 28- PDF

Nonconvergence to Unstable Points in Urn Models and Stochastic Approximations

- R. Pemantle
- Mathematics
- 1 April 1990

A particle in Rd moves in discrete time. The size of the nth step is of order 1/n and when the particle is at a position v the expectation of the next step is in the direction F(v) for some fixed… Expand

230 24

A survey of random processes with reinforcement

- R. Pemantle
- Mathematics
- 2 October 2006

The models surveyed include generalized Polya urns,
reinforced random walks, interacting urn models, and
continuous reinforced processes. Emphasis is on methods and
results, with sketches provided… Expand

423 23- PDF

Ergodic theory on Galton—Watson trees: speed of random walk and dimension of harmonic measure

- R. Lyons, R. Pemantle, Y. Peres
- Mathematics
- 1 June 1995

We consider simple random walk on the family tree T of a nondegenerate supercritical Galton—Watson branching process and show that the resulting harmonic measure has a.s. strictly smaller Hausdorff… Expand

172 23- PDF

Random walk in a random environment and rst-passage percolation on trees

- R. Lyons, R. Pemantle
- Computer Science, Mathematics
- 2 April 2004

TLDR

79 23

Towards a theory of negative dependence

- R. Pemantle
- Mathematics
- 3 March 2000

The FKG theorem says that the positive lattice condition, an easily checkable hypothesis which holds for many natural families of events, implies positive association, a very useful property. Thus… Expand

161 22- PDF

Biased random walks on Galton–Watson trees

- R. Lyons, R. Pemantle, Y. Peres
- Mathematics
- 2 October 1996

Summary. We consider random walks with a bias toward the root on the family tree T of a supercritical Galton–Watson branching process and show that the speed is positive whenever the walk is… Expand

113 20- PDF

First passage percolation and a model for competing spatial growth

- O. Haggstrom, R. Pemantle
- Mathematics
- 23 January 1997

An interacting particle system modelling competing growth on the ℤ 2 lattice is defined as follows. Each x ∈ ℤ 2 is in one of the states {0,1,2}. 1's and 2's remain in their states for ever, while a… Expand

91 19- PDF