arXiv subjects

Sam McKeown

Publications and source records attributed to Sam McKeown.

3 recordsLinked to original sources

arXiv2026

On the most likely geodesic in last passage percolation

We consider the problem of identifying the paths most likely to occur as geodesics in last passage percolation. Heuristics suggest that these modal paths should be the extreme corner paths, going straight between the corners of the cube of accessible vertices. We identify three mechanisms which favour such corner paths, and show that they are more likely to appear than all but a vanishingly small portion of paths. We make more specific comparisons in exponential last passage percolation, where moderate deviation estimates may be used to show that corner paths are nearly modal in a precise sense. Finally, we show a form of monotonicity of geodesic probabilities in a special case and conjecture that this holds in general.

math.PR↗

arXiv2025

The Busemann Process and Steep Highways in Directed First Passage Percolation

We consider the Busemann process in planar directed first passage percolation. We extend existing techniques to establish the existence of the process in our setting and determine its distribution in a number of integrable models. As examples of their utility, we show how these explicit distributions may be used to quantify the semi-infinite geodesics passing through thin rectangles, and the clustering phenomenon observed in competition interface angles. There is a natural connection with various particle systems, and in particular we obtain the multi-class invariant distributions for discrete-time TASEP with parallel updates.

math.PR↗

arXiv2025

Near-the-Axis Universality in Last Passage Percolation

This note establishes a universal directed landscape limit for last passage percolation models in an intermediate scaling regime. We find as a quick consequence the transversal fluctuations for geodesics taken near the axis. We extend the technique of Bodineau and Martin, who in arXiv:math/0410042 have already shown universal one-point fluctuations in this regime.

math.PR↗