3 papers
math.PR2025
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…
math.CO2025
Modified Macdonald polynomials and the multispecies zero range process: II
Arvind Ayyer, Olya Mandelshtam, James B. Martin
In a previous part of this work, we gave a new tableau formula for the modified Macdonald polynomials , using a weight on tableaux involving the \emph{queu…
math.PR2024
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…