85 citations · 124 across the 6 of their papers we have counts for
5 papers · 1 filter
The Jammed Phase of the Biham-Middleton-Levine Traffic Model
Omer Angel, Alexander E Holroyd, James B Martin
Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites…
Random recursive trees and the Bolthausen-Sznitman coalescent
Christina Goldschmidt, James B. Martin
We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the fin…
A universality property for last-passage percolation paths close to the axis
Thierry Bodineau, James B. Martin
We consider a last-passage directed percolation model in , with i.i.d. weights whose common distribution has a finite th moment. We study the fluctuations of the pass…
Reconstruction thresholds on regular trees
James B. Martin
We consider a branching random walk with binary state space and index set , the infinite rooted tree in which each node has k children (also known as the model of "broadcastin…
Limiting shape for directed percolation models
James B. Martin
We consider directed first-passage and last-passage percolation on the nonnegative lattice Z_+^d, d\geq2, with i.i.d. weights at the vertices. Under certain moment conditions on th…