Matrix norms and rapid mixing for spin systems
نویسندگان
چکیده
منابع مشابه
Matrix norms and rapid mixing for spin systems
We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the associated dependency matrix is less than 1. We give improved analysis for the case in which the diagonal of the dependency matrix is 0 (as in heat bath dynamics...
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For anti-ferromagnetic 2-spin systems, a beautiful connection has been established, namely that the following three notions align perfectly: the uniqueness of Gibbs measures in infinite regular trees, the decay of correlations (also known as spatial mixing), and the approximability of the partition function. The uniqueness condition implies spatial mixing, and an FPTAS for the partition functio...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2009
ISSN: 1050-5164
DOI: 10.1214/08-aap532