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Limiting shape for directed percolation models

- James B. Martin
- Mathematics
- 7 January 2003

We consider directed first-passage and last-passage percolation on the nonnegative lattice Z d + , d ≥ 2, with i.i.d. weights at the vertices. Under certain moment conditions on the common… Expand

Random Recursive Trees and the Bolthausen-Sznitman Coalesent

- C. Goldschmidt, James B. Martin
- Mathematics
- 13 February 2005

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 final collision of the… Expand

Stationary distributions of multi-type totally asymmetric exclusion processes

- P. Ferrari, James B. Martin
- Mathematics
- 19 January 2005

We consider totally asymmetric simple exclusion processes with n types of particle and holes (n-TASEPs) on Z and on the cycle Z N . Angel recently gave an elegant construction of the stationary… Expand

Coagulation-fragmentation duality, Poisson-Dirichlet distributions and random recursive trees

- R. Dong, C. Goldschmidt, James B. Martin
- Mathematics
- 28 July 2005

In this paper we give a new example of duality between fragmentation and coagulation operators. Consider the space of partitions of mass (i.e., decreasing sequences of nonnegative real numbers whose… Expand

A Universality Property for Last-Passage Percolation Paths Close to the Axis

- T. Bodineau, James B. Martin
- Mathematics
- 3 October 2004

We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the… Expand

Heavy tails in last-passage percolation

- B. Hambly, James B. Martin
- Mathematics
- 8 April 2006

AbstractWe consider last-passage percolation models in two dimensions, in which the underlying weight distribution has a heavy tail of index α < 2. We prove scaling laws and asymptotic distributions,… Expand

A phase transition for competition interfaces

- P. Ferrari, James B. Martin, Leandro P. R. Pimentel
- Mathematics
- 15 January 2007

We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this… Expand

Reconstruction Thresholds on Regular Trees

- James B. Martin
- MathematicsDRW
- 28 May 2003

TLDR

Discrete low-discrepancy sequences

- Omer Angel, A. Holroyd, James B. Martin, J. Propp
- Mathematics
- 6 October 2009

Holroyd and Propp used Hall's marriage theorem to show that, given a probability distribution pi on a finite set S, there exists an infinite sequence s_1,s_2,... in S such that for all integers k >=… Expand

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