{"product_id":"9789814513395","title":"Gibbs Measures On Cayley Trees","description":"\u003cp\u003eThe purpose of this book is to present systematically all known mathematical results on Gibbs measures on Cayley trees (Bethe lattices).\u003c\/p\u003e \u003cp\u003eThe Gibbs measure is a probability measure, which has been an important object in many problems of probability theory and statistical mechanics. It is the measure associated with the Hamiltonian of a physical system (a model) and generalizes the notion of a canonical ensemble. More importantly, when the Hamiltonian can be written as a sum of parts, the Gibbs measure has the Markov property (a certain kind of statistical independence), thus leading to its widespread appearance in many problems outside of physics such as biology, Hopfield networks, Markov networks, and Markov logic networks. Moreover, the Gibbs measure is the unique measure that maximizes the entropy for a given expected energy.\u003c\/p\u003e \u003cp\u003eThe method used for the description of Gibbs measures on Cayley trees is the method of Markov random field theory and recurrent equations of this theory, but the modern theory of Gibbs measures on trees uses new tools such as group theory, information flows on trees, node-weighted random walks, contour methods on trees, and nonlinear analysis. This book discusses all the mentioned methods, which were developed recently.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e \u003cul\u003e \u003cli\u003eGroup Representation of the Cayley Tree\u003c\/li\u003e \u003cli\u003eIsing Model on the Cayley Tree\u003c\/li\u003e \u003cli\u003eIsing Type Models with Competing Interactions\u003c\/li\u003e \u003cli\u003eInformation Flow on Trees\u003c\/li\u003e \u003cli\u003eThe Potts Model\u003c\/li\u003e \u003cli\u003eThe Solid-on-Solid Model\u003c\/li\u003e \u003cli\u003eModels with Hard Constraints\u003c\/li\u003e \u003cli\u003ePotts Model with Countable Set of Spin Values\u003c\/li\u003e \u003cli\u003eModels with Uncountable Set of Spin Values\u003c\/li\u003e \u003cli\u003eContour Arguments on Cayley Trees\u003c\/li\u003e \u003cli\u003eOther Models\u003c\/li\u003e \u003c\/ul\u003e  \u003cbr\u003e \u003cb\u003eReadership:\u003c\/b\u003e Researchers in mathematical physics, statistical physics, probability and measure theory.\u003cb\u003eKey Features:\u003c\/b\u003e  \u003cul\u003e \u003cli\u003eThe book is for graduate, post-graduate students and researchers. This is the first book concerning Gibbs measures on Cayley trees\u003c\/li\u003e \u003cli\u003eIt can be used to teach special courses like “Gibbs measures on countable graphs”, “Models of statistical physics”, “Phase transitions and thermodynamics” and many related courses\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47185291739376,"sku":"9789814513395","price":51.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814513395_p0.jpg?v=1763691951","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814513395","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}