December 10, 2010
Location: Janskerkhof 15a (Utrecht), room 101
Large deviations for nonequilibrium purposes
Fluctuation theory is at the heart of statistical mechanics. We discuss the relevance of the occupation fluctuations in clarifying the nature of entropy production principles, in providing a Liapunov function for the relaxation towards nonequilibrium, and for amending the standard fluctuation-dissipation theorem. These basic concepts and results can already by explained for Markov processes with finite state space, but we aim at their relevance for spatially extended systems.
Joint work with many people; see also my webpage for the relevant papers.
Random walk in dynamic random environment
We consider an interacting particle system on the integer lattice in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on vacant sites has a local drift to the left. We describe some recent results for the empirical speed of the walk (law of large numbers, central limit theorem, and large deviation principle) for different choices of the interacting particle system. We compare these results with what is known for static random environments, describe recent extensions, and list open problems.
Based on joint work with Luca Avena, Frank Redig, Renato dos Santos and Vladas Sidoravicius.