“Hydrodynamics for the partial exclusion process in random environment via stochastic duality”
Mercoledì 21 Dicembre 2022, ore 11:00 - Aula 2AB45 e Zoom - Simone Floreani (University of Oxford)
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.