From diffusive to fractional behavior in a boundary driven exclusion process
Year: 2020
Type: preprint
Abstract: The purpose of this article is to study the hydrodynamic limit of the symmetric exclusion process with long jumps and in contact with infinitely extended reservoirs for a particular critical regime. The jumps are given in terms of a transition probability that can have finite or infinite variance and the hydrodynamic equation is a diffusive equation, in the former case, or a fractional equation, in the latter case. In this work we treat the critical case, that is, when the variance is infinite but of logarithm order wrt the system size. This is the case in which there is a transition from diffusive to super-diffusive behavior.
Source: arXiv (Cornell University)
Authors: Patrícia Gonçalves, Stefano Scotta
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3015520004