Dear Colleagues,
We would like to invite you to the following SPASS seminars, jointly organized by UniPi, SNS, UniFi and UniSi:
The Smoluchowski-Kramers diffusion-approximation for a class of constrained stochastic wave equations
Sandra Cerrai (University of Maryland)
Metastability for the Potts model with Glauber dynamics
Gianmarco Bet (University of Florence)
The seminars will take place on TUE, 20.6.2023, respectively at 14:00 CET and at 15:00 CET in Sala Seminari, Dipartimento di Matematica, 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
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Abstract (Cerrai at 14:00): We investigate the well-posedness of a class of stochastic second-order in time-damped evolution equations in Hilbert spaces, subject to the constraint that the solution lies within the unitary sphere. Then, we focus on a specific example, the stochastic damped wave equation in a bounded domain of a d-dimensional Euclidean space, endowed with the Dirichlet boundary condition, with the added constraint that the L^2-norm of the solution is equal to one. We introduce a small mass mu>0 in front of the second-order derivative in time and examine the validity of a Smoluchowski-Kramers diffusion approximation. We demonstrate that, in the small mass limit, the solution converges to the solution of a stochastic parabolic equation subject to the same constraint. We further show that an extra noise-induced drift emerges, which in fact does not account for the Stratonovich-to-Itô correction term.
Abstract (Bet 15:00): In this talk, I will describe some recent result on the low-temperature metastabile behavior of the ferromagnetic Potts model on a finite two-dimensional grid-graph Λ, evolving according to Glauber dynamics. More specifically, to each spin configuration is associated an energy that depends on local spin alignment, as well as on an external magnetic field that acts only on one spin value. We describe separately the case of negative, positive and, if time allows, zero external magnetic field. In the first case there are q − 1 stable configurations and a unique metastable state. In the second case there are q − 1 symmetric metastable configurations and only one global minimum. In the third scenario the system has q stable equilibria. In the negative and positive cases we study the asymptotic behavior of the first hitting time from the metastable to the stable state as the inverse temperature tends to infinity. Moreover, in both cases we identify the union of gates and prove that this union has to be crossed with high probability during the transition. Based on joint work with Anna Gallo and Francesca Nardi.