Dear Colleagues,

We would like to invite you to the "Padova Seminars in Probability and Finance seminar" that will take place on March 6th, 2023 at 16.00, Room 1BC45 at the department of Mathematics “Tullio Levi-Civita". The seminar will be held in person and online via the Zoom platform.

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Speaker: Alessandra Faggionato (Università La Sapienza)

Title: Hydrodynamic limit of simple exclusion processes on point processes with random conductances

Date and time: Monday, MARCH 6th at 16.00 Place: room 1BC45 at the Department of Mathematics, University of Padova Zoom link: https://unipd.zoom.us/j/83774362817?pwd=ZDZnRGdZZGpDNDRQd3pMQUw4NUx4dz09 available also on the webpage https://www.math.unipd.it/~bianchi/seminari/

Abstract: We consider continuous-time random walks on a simple point process with random symmetric jump rates. The jump range can be unbounded. We assume some second-moment conditions and that the above randomness is left invariant by the action of the group G = R^d or G = Z^d. We then add the site-exclusion interaction, thus making the particle system a simple exclusion process. We show that, for almost all environments, under diffusive space-time rescaling the system exhibits a hydrodynamic limit in path space. The hydrodynamic equation is non-random and governed by the effective homogenized matrix D of the single random walk, which can be degenerate. The proof relies both on particle duality and on stochastic homogenization for a single random walk. We then focus on specific examples, including the simple exclusion process on Delaunay triangulations.

With best regards, Alberto Chiarini

Department of Mathematics Tullio Levi-Civita Via Trieste 63 35121 Padova Italy