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October 10, 2012
"Surprises in nonequilibrium Statistical Mechanics''
WEDNESDAY OCTOBER 10
Roberto Fernandez A regular process that is non gibbssian Processes are determined by transition probabilities, that
is by conditional expectations with respect to the past. In contrast,
onedimensional Gibbs measures are fields determined by simultaneous
conditioning on past and future. For Markovian and exponentially continuous
processes both theories are known to be equivalent. Frank den Hollander Renormalization of hierarchically interacting Cannings processes In order to analyse universal patterns in the large
spacetime behaviour of interacting multitype stochastic populations, a key
approach has been to carry out a renormalization analysis in the hierarchical
meanfield limit. This has provided considerable insight into the structure of
interacting systems of diffusions. Errico Presutti Symmetric simple exclusion process (SSEP) with births and deaths and convergence to a Stefan problem I will describe some preliminary results obtained in collaboration with Anna De Masi and Pablo Ferrari on the symmetric simple exclusion process (SSEP) on Z with births and deaths. We consider configurations where there are finitely many particles to the right of the origin and finitely many holes to its left. The evolution is SSEP at rate 1/2 plus birth death processes each one at rate $\epsilon$,. The birth is given by the first hole being replaced by a particle and the death by the last particle being replaced by a hole. We prove the existence of a unique invariant measure as seen from the first hole and prove that the average distance between last particle and first hole scale as $\epsilon^{1}$. We also show that the macroscopic limit is described by a Stefan (free boundary) problem. Frank Redig Dynamics of the condensate in the symmetric inclusion process The symmetric inclusion process is a particle system where particles perform random walks on a lattice, and interact by attracting each other. If, on a fixed finite lattice, the rate of random walk is converging to zero, and at the same time many particles are in the system, condensation phenomena occur. We study the asymptotic dynamics of these condensates. In the fully connected case, a single condensate is formed immediately, and hops randomly over the lattice. In the non fully connected case, several condensates form and merge according to a diffusive dynmics to form eventually a single condensate. (joint work with Stefan Grosskinsky (Warwick) and Kiamars Vafayi (Eindhoven))
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