The topological strong spatial mixing property and new conditions for\n pressure approximation

2014/11/09 by Raimundo Briceño, Briceño, Raimundo
Mathematics · Chemistry · Environmental Science · #Markov Chains and Monte Carlo Methods #Mass Spectrometry Techniques and Applications #Isotope Analysis in Ecology

paper · pdf · doi:10.48550/arxiv.1411.2289

Abstract

In the context of stationary \ℤ^d nearest-neighbour Gibbs measures\n\μ satisfying strong spatial mixing, we present a new combinatorial\ncondition (the topological strong spatial mixing property (TSSM)) on the\nsupport of \μ sufficient for having an efficient approximation algorithm for\ntopological pressure. We establish many useful properties of TSSM for studying\nstrong spatial mixing on systems with hard constraints. We also show that TSSM\nis, in fact, necessary for strong spatial mixing to hold at high rate. Part of\nthis work is an extension of results obtained by D. Gamarnik and D. Katz\n(2009), and B. Marcus and R. Pavlov (2013), who gave a special representation\nof topological pressure in terms of conditional probabilities.\n

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