The Busemann process of (1+1)-dimensional directed polymers 

Directed polymers are a statistical mechanics model for random growth.  Their partition functions collectively form a solution to a discrete stochastic heat equation.  This talk will discuss ratios of partition functions, which lead to solutions of a discrete stochastic Burgers equation.  Of interest is the success or failure of the “one force-one solution principle” for this equation.  I will reframe this question in the language of polymers, and share some surprising results that follow.  Based on joint work with Louis Fan and Timo Seppäläinen.