Technical Terms Partition Function: A sum over all possible states of a system, each weighted by an exponential factor related to its energy, which encapsulates the system’s statistical properties.

We introduce a random walk in random environment associated to an underlying directed polymer model in 1 + 1 dimensions. This walk is the positive temperature counterpart of the competition interface ...

This article gives a proof of the Langlands-Shelstad fundamental lemma for the spherical Hecke algebra for every unramified p-adic reductive group G in large positive characteristic. The proof is ...

Additionally, foundational investigations into the complexity of approximating complex-valued partition functions have reinforced the pivotal role of these functions in bridging statistical ...