121 citations · 397 across the 32 of their papers we have counts for
33 papers · 1 filter
Permutation invariance in last-passage percolation and the distribution of the Busemann process
Erik Bates, Elnur Emrah, James Martin +2
In i.i.d. exponential last-passage percolation, we describe the joint distribution of Busemann functions, over all edges and over all directions, in terms of a joint last-passage p…
Convergence of the Environment Seen from Geodesics in Exponential Last-Passage Percolation
James B. Martin, Allan Sly, Lingfu Zhang
A well-known question in planar first-passage percolation concerns the convergence of the empirical distribution of weights as seen along geodesics. We demonstrate this convergence…
The TAZRP speed process
Gideon Amir, Ofer Busani, Patrícia Gonçalves +1
In [AAV] Amir, Angel and Valk{ó} studied a multi-type version of the totally asymmetric simple exclusion process (TASEP) and introduced the TASEP speed process, which allowed them…
Galton-Watson games
Alexander E. Holroyd, James B. Martin
We consider two-player combinatorial games in which the graph of positions is random and perhaps infinite, focusing on directed Galton-Watson trees. As the offspring distribution i…
Stationary distributions of the multi-type ASEP
James B. Martin
We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line . The construction c…
Minimax functions on Galton-Watson trees
James B. Martin, Roman Stasiński
We consider the behaviour of minimax recursions defined on random trees. Such recursions give the value of a general class of two-player combinatorial games. We examine in particul…