Spatial mixing: Refinements and Applications

Recardo Restrepo (mentor: Prasad Tetali, Math+CS) - The hard-core model in a graph G, is a parametric measure of the independent sets of the graph in which the 'fugacity' parameter favors greater independent sets as it increases. Sampling instances of the hard-core model is an interesting problem which, in the case of general graphs of bounded degree, follows a transition from computational `easy' to `hard' (Weitz 2006, Sly 2010). We are interested in to explore such situation for the hard-core model in the particular case of the n x n square lattice through the study of the property known as Strong Spatial Mixing (Dyer, Sinclair, Vigoda and Weitz 2004). Also, we study its extension to multi-spin models (Nair and Tetali) and its implications for MCMC sampling.