Filters

20202

More filters

20222
Reset filters

Settings

Author: Gabrielli, Davide × End date: 2024 × Start date: 2020 × Subject: Large deviations × WGL Institute: WIAS ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Dynamical Phase Transitions for Flows on Finite Graphs
    (New York, NY [u.a.] : Springer Science + Business Media B.V., 2020) Gabrielli, Davide; Renger, D.R. Michiel
    We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation involving paths of the density and flow. We give sufficient conditions under which the large deviations of a given time averaged flow is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.
  • Thumbnail Image
    Item
    Dynamical phase transitions for flows on finite graphs
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Gabrielli, Davide; Renger, D. R. Michiel
    We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation involving paths of the density and flow. We give sufficient conditions under which the large deviations of a given time averaged flow is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.