Francesco Caravenna

We investigate the concept of noise sensitivity for functionals of i.i.d. random variables, which refers to the property that a small perturbation in the underlying randomness leads to an asymptotically independent functional. We extend classical noise sensitivity criteria beyond the Boolean setting, deriving quantitative estimates with optimal rates.

As an application, we consider the model of directed polymers in random environments, which describes a random walk interacting with a random medium. In the critical dimension $d=2$, under a critical rescaling of the noise strength, the partition function of the model is known to converge to a universal limit, the Stochastic Heat Flow. We show that in this regime, the partition function exhibits noise sensitivity.

(Based on joint work with Anna Donadini)