Dear Colleagues,

We would like to invite you to the "Padova Seminars in Probability and Finance seminar" that will take place on December 21st at 11.00 in Padova in room 2AB45 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: Simone Floreani (University of Oxford)

Title: Hydrodynamics for the partial exclusion process in random environment via stochastic duality

Date and time: Wednesday, DECEMBER 21st at 11.00 Place: room 2AB45 at the Department of Mathematics, University of Padova Zoom link: https://unipd.zoom.us/j/88295505400 available also on the webpage https://www.math.unipd.it/~bianchi/seminari/

Abstract: In this talk, I present a partial exclusion process in random environment, a system of random walks where the random environment is obtained by assigning a maximal occupancy to each site of the Euclidean lattice. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. After recalling some results on the Bouchaud's trap model, I will show that, when assuming that the maximal occupancies are heavy tailed and i.i.d., the hydrodynamic limit of the particle system is the fractional-kinetics equation. The strategy of the proof is based on stochastic duality, a useful tool in probability theory which allows to study a Markov process (the one that interests you) via another one, called dual process, which is hopefully simpler. In the final part of the talk, I will focus on how some duality relations can be obtained in a more general framework.

With best regards, Alberto Chiarini

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