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Integrable directed polymers and their stationary measures
Abstract
Directed polymers are an important family of models in the Kardar–Parisi–Zhang (KPZ) universality class, providing a probabilistic framework for studying random interface growth and disordered systems. However, exact statistical results are available only for models with specially chosen disorders, known as the integrable ones.
This talk will present several integrable directed polymer models in different space–time geometries, with a focus on their stationary measures. We will explain how these stationary structures can be used to deduce laws of large numbers for the corresponding free energies. Time permitting, we will also discuss recent developments on polymer models with matrix-valued disorder, based on joint work with Guillaume Barraquand.
