Dear Colleagues,
We would like to invite you to the following (double) SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi (abstracts below):
*Weak coupling scaling of critical SPDEs* by *Giuseppe Cannizzaro *(University of Warwick)
*Sharp asymptotics for the Allen-Cahn equation in the limit of small noise and large volume* by* Giacomo di Gesù* (La Sapienza)
The seminars will take place on *TUE, 19.9.2023* respectively at *14:00 CET and 15:00 CET *in Aula Seminari, Dipartimento di Matematica, University of Pisa and streamed online at the link below.
The organizers, A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass https://www.google.com/url?q=https://sites.google.com/unipi.it/spass&source=gmail-imap&ust=1665669490000000&usg=AOvVaw07o0tKOUGmZjDDF2Ta7pQY
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*Weak coupling scaling of critical SPDEs*
Abstract: The study of stochastic PDEs has known tremendous advances in recent years and, thanks to Hairer's theory of regularity structures and Gubinelli and Perkowski's paracontrolled approach, (local) existence and uniqueness of solutions of subcritical SPDEs is by now well-understood. The goal of this talk is to move beyond the aforementioned theories and present novel tools to derive the scaling limit (in the so-called weak coupling scaling) for some stationary SPDEs at the critical dimension. Our techniques are inspired by the resolvent method developed by Landim, Olla, Yau, Varadhan, and many others, in the context of particle systems in the supercritical dimension and might be well-suited to study a much wider class of statistical mechanics models at criticality.
*Sharp asymptotics for the Allen-Cahn equation in the limit of small noise and large volume*
Abstract: We consider the Allen-Cahn equation on a finite interval perturbed by space-time white noise. Keeping the size of the spatial domain fixed, the dynamics becomes metastable in the limit of vanishing noise. I will review some sharp metastability estimates in this regime and discuss how the invariant measure and long-time behavior is affected if one allows the system size to grow while the noise vanishes (joint work with L. Bertini and P. Buttà).