Toronto Probability

Polymers in disordered media are examples of random Gibbs measures on paths traversing a random environment. Such disordered systems often exhibit intricate energy landscapes rich with multiple valleys corresponding to metastable states. This generic property makes a system fragile and extremely sensitive to perturbations. Namely, a slight variation in external parameters such as the disorder or the temperature causes a profound change in the system, a phenomenon known as chaos. In experimental studies of chaos, temperature is the prototypical control parameter as it is easier to vary than the disorder. However, on the mathematical side, studying disorder chaos is easier as perturbing the disorder amounts to infusing the system with extra independent randomness.

In this talk we will report the first progress in understanding temperature chaos in the Kardar–Parisi–Zhang universality class, with the Continuum Directed Random Polymer being the model of study. Time permitting, we will also touch upon an application to noise sensitivity in the Directed Landscape, and outline a connection between temperature and disorder chaos. This is joint work with Shirshendu Ganguly and Zoe Himwich (https://arxiv.org/abs/2607.18194).