Filters

2016 - 20202

More filters

20222
Reset filters

Settings

Has files: Yes × Publisher: New York, NY [u.a.] : Springer Science + Business Media B.V. × 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
    Large Deviations of Continuous Regular Conditional Probabilities
    (New York, NY [u.a.] : Springer Science + Business Media B.V., 2016) van Zuijlen, W.
    We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a sequence of probability measures on the product space that satisfies a large deviation principle, we present necessary and sufficient conditions for the conditional probabilities under these measures to satisfy a large deviation principle. The arguments of these conditional probabilities are assumed to converge. A way to view regular conditional probabilities as a special case of product regular conditional probabilities is presented. This is used to derive conditions for large deviations of regular conditional probabilities. In addition, we derive a Sanov-type theorem for large deviations of the empirical distribution of the first coordinate conditioned on fixing the empirical distribution of the second coordinate.