Probability Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- 36 English Building
- Date
- Oct 22, 2024 2:00 - 2:50 pm
- Speaker
- Christopher Janjigian (Purdue)
- Contact
- Xuan Wu
- xuanw@illinois.edu
- Views
- 33
Title: Infinite geodesic in inhomogeneous exponential last passage percolation.
Abstract: This talk will discuss some recent progress in 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 with Elnur Emrah (Bristol) and Timo Seppäläinen (Madison)