Représentation du champ de fluctuation de diffusions indépendantes par le drap brownien
Aging for interacting diffusion processes
The quenched invariance principle for random walks in random environments admitting a bounded cycle representation
We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman ( (2004) 219–244) to the non-reversible setting.
Markovian perturbation, response and fluctuation dissipation theorem
We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of “linear response function” in the general framework of Markov processes. We show that for processes out of equilibrium it depends not only on the given Markov process () but also on the chosen perturbation of it. We characterize the set of all possible response functions for a given Markov process and show that at equilibrium they all satisfy the FDT. That is,...
Decay of covariances, uniqueness of ergodic component and scaling limit for a class of systems with non-convex potential
We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. Using a technique which decouples the neighboring vertices into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for -Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.
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