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math.PR2026
Negative association of Busemann functions in exponential last-passage percolation
Erik Bates, Xiao Shen
One hallmark of exactly solvable KPZ random growth models is product-form invariant measures. In the setting of exponential last-passage percolation (LPP), this corresponds to the…
math.PR2025
An upper bound on geodesic length in 2D critical first-passage percolation
Erik Bates, David Harper, Xiao Shen +1
We consider i.i.d. first-passage percolation (FPP) on the two-dimensional square lattice, in the critical case where edge-weights take the value zero with probability $\tfrac{1}{2}…
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…