Directed polymers are a statistical mechanics model for random growth. Their partition functions are solutions to a discrete stochastic heat equation. This talk will discuss the logarithmic derivatives of the partition functions, which are solutions to 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.
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