Recent years have seen a great deal of progress in understanding the behavior of bootstrap percolation (BP) models, a particular class of monotone cellular automata. In the initial configuration sites are occupied with probability p. The evolution of BP occurs at discrete times: empty sites stay empty and occupied sites are emptied iff a certain model dependent neighborhood is already empty....

Consider a system of N particles, described via a system of Stochastic Differential Equations (SDEs), interacting in a mean field way. We are interested in the limit, as N goes to infinity, of this particle system, and try to derive from a microscopic point of view (i.e. particle dynamics) a mesoscopic point of view (i.e. a statistical description of the system). The notion of propagation of...

The string-net models were introduced by Levin and Wen (1) as exactly solvable models of topological order in two dimensions. The latter appears in strongly interacting or frustrated systems and is characterized by the presence of point-like excitations, called anyons, with exotic (i.e. neither fermionic nor bosonic) exchange statistics. Built from a unitary fusion category, the string-net...