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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Hydrodynamics for the partial exclusion process in random environment

## Hydrodynamics for the partial exclusion process in random environmentAdd to your list(s) Download to your calendar using vCal - Simone Floreani (Delft University of Technology)
- Friday 25 February 2022, 14:30-15:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. FD2W01 - Deterministic and stochastic fractional diﬀerential equations and jump processes 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. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we prove that the quenched hydrodynamic limit is a heat equation with a homogenized diffusion matrix. To this purpose, we exploit the stochastic self-duality property to transfer a homogenization result concerning random walks in the same environment with arbitrary starting points to the particle system. In the second part of the talk, I will discuss some open questions occurring when removing the uniform ellipticity assumption. 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., we expect as hydrodynamic limit the fractional-kinetics equation. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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