# Probability and Mathematical Physics Seminar

#### Infinite geodesics and Busemann functions in inhomogeneous exponential last passage percolation

**Speaker:**
Christopher Janjigian, Purdue University

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, May 3, 2024, 11:10 a.m.

**Synopsis:**

This talk will discuss some recent progress on understanding the structure of semi-infinite geodesics and their associated Busemann functions in the inhomogeneous exactly solvable exponential last-passage percolation model. In contrast to the homogeneous model, this generalization admits linear segments of the limit shape and an associated richer structure of semi-infinite geodesic behaviors. Depending on certain choices of the inhomogeneity parameters, we show that the model exhibits new behaviors of semi-infinite geodesics, which include wandering semi-infinite geodesics with no asymptotic direction, isolated asymptotic directions of semi-infinite geodesics, and non-trivial intervals of directions with no semi-infinite geodesics.

Based on joint work-in-progress with Elnur Emrah (Bristol) and Timo Seppäläinen (Madison)