Francesco Caravenna

We consider the (ill-defined) 2d Stochastic Heat Equation with multiplicative space-time white noise. Upon discretisation of space-time, the solution coincides with the partition function of 2d directed polymers in random environment: under a critical (logarithmic) rescaling of the noise strength, it converges to a universal limit known as the critical 2d Stochastic Heat Flow. We prove that discretised solution (or partition function) is noise sensitive, i.e. any small perturbation of the underlying noise produces a solution which becomes asymptotically independent of the original one. This is obtained by generalising classical criteria for noise sensitivity beyond the boolean setting, which have an independent interest. As a corollary, the Stochastic Heat Flow is shown to be independent of the white noise driving the corresponding Stochastic Heat Equation. (Based on joint work with Anna Donadini)

Noise sensitivity for 2d Stochastic Heat Equation and directed polymers

.pdf [20361Kb]