Student Probability Seminar

---

The Shape Function for Optimal Paths in Random Environments

Speaker: Douglas Dow, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, March 20, 2023, 1:15 p.m.

Synopsis:

When evaluating a potential route for a road trip one might take into consideration the sum of the coolness of the environment one passes by and the cost (in time or gas) one pays for travelling away from the quickest route. More abstractly, one could try to understand the large scale, universal properties of paths that minimize a given energy in a random environment. We will take the environment to be a random field and study the behavior of the minimal action as the lengths of these paths gets very large. I will define the so-called shape function—the limiting average action that the minimizing paths accrue when travelling with a given average speed v--and discuss an approach to proving differentiability of the shape function with respect to the average speed. Based on joint work with Yuri Bakhtin.