Seminari (PMS)^2 - Deuschel

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Giovedì 4 maggio alle ore 16:30, per il ciclo

(PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics
 
coorganizzato dalle università Milano-Bicocca, Pavia e Milano-Politecnico, in aula 3014 Jean-Dominique Deuschel (TU Berlin) parlerà di

Title: An isomorphism theorem for Ginzburg-Landau interface models and scaling limits.  

AbstractWe introduce a natural measure on bi-infinite random walk trajectories evolving in a time-dependent environment driven by the Langevin dynamics associated with a gradient Gibbs measure with convex potential. We derive an identity relating the occupation times of the Poissonian cloud induced by this measure to the square of the corresponding gradient field, which - generically - is not Gaussian. In the quadratic case, we recover a well-known generalization of the second Ray-Knight theorem. We further determine the scaling limits of the various objects involved in dimension 3, which are seen to exhibit homogenization. In particular, we prove that the renormalized square of the gradient field converges under appropriate rescaling to the Wick-ordered square of a Gaussian free field on R^3 with suitable diffusion matrix, thus extending a celebrated result of Naddaf and Spencer regarding the scaling limit of the field itself. (Based on joint work with Pierre-François Rodriguez.)
 
Place: Aula 3014, Dip. di Matematica e Applicazioni, Univ. di Milano-Bicocca, via R. Cozzi 55, Milano
Webex link:
https://unimib.webex.com/unimib-it/j.php?MTID=mc07da73e64ea2eb0da78975bc808f3db
Meeting number:
2741 491 0178
Password:
HPxNQASR579 (47967277 for phones)
 
 
Participation is free and welcome!
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