Gibbs Measures on Cayley Trees by Utkir A Rozikov

By Utkir A Rozikov

The function of this booklet is to provide systematically all identified mathematical effects on Gibbs measures on Cayley timber (Bethe lattices).

The Gibbs degree is a likelihood degree, which has been an enormous item in lots of difficulties of likelihood thought and statistical mechanics. it's the degree linked to the Hamiltonian of a actual process (a version) and generalizes the proposal of a canonical ensemble. extra importantly, while the Hamiltonian should be written as a sum of components, the Gibbs degree has the Markov estate (a definite type of statistical independence), therefore resulting in its common visual appeal in lots of difficulties open air of physics akin to biology, Hopfield networks, Markov networks, and Markov good judgment networks. in addition, the Gibbs degree is the original degree that maximizes the entropy for a given anticipated energy.

The process used for the outline of Gibbs measures on Cayley bushes is the strategy of Markov random box concept and recurrent equations of this idea, however the sleek thought of Gibbs measures on bushes makes use of new instruments akin to staff conception, details flows on bushes, node-weighted random walks, contour tools on bushes, and nonlinear research. This booklet discusses all of the pointed out equipment, which have been built recently.


  • Group illustration of the Cayley Tree
  • Ising version at the Cayley Tree
  • Ising sort versions with Competing Interactions
  • Information circulation on Trees
  • The Potts Model
  • The Solid-on-Solid Model
  • Models with demanding Constraints
  • Potts version with Countable Set of Spin Values
  • Models with Uncountable Set of Spin Values
  • Contour Arguments on Cayley Trees
  • Other Models

Readership: Researchers in mathematical physics, statistical physics, likelihood and degree theory.Key Features:

  • The ebook is for graduate, post-graduate scholars and researchers. this can be the 1st booklet pertaining to Gibbs measures on Cayley trees
  • It can be utilized to educate particular classes like “Gibbs measures on countable graphs”, “Models of statistical physics”, “Phase transitions and thermodynamics” and lots of similar courses

Show description

Read or Download Gibbs Measures on Cayley Trees PDF

Similar mathematical physics books

Mastering Your PhD: Survival and Success in the Doctoral Years and Beyond

"Mastering Your PhD: Survival and good fortune within the Doctoral Years and past" is helping consultant PhD scholars via their graduate scholar years. packed with functional recommendation on getting all started, speaking together with your manager, staying the direction, and making plans for the long run, this publication is a convenient advisor for graduate scholars who want that additional little bit of aid getting began and making it via.

Statistical Physics of Fields

Whereas many scientists are acquainted with fractals, fewer are conversant in scale-invariance and universality which underlie the ubiquity in their shapes. those homes may well emerge from the collective behaviour of easy primary ingredients, and are studied utilizing statistical box theories. preliminary chapters attach the particulate standpoint built within the significant other quantity, to the coarse grained statistical fields studied right here.

Theoretical Concepts in Physics: An Alternative View of Theoretical Reasoning in Physics

A hugely unique, and actually novel, method of theoretical reasoning in physics. This ebook illuminates the topic from the viewpoint of actual physics as practised through learn scientists. it truly is meant to be a complement to the ultimate years of an undergraduate path in physics and assumes that the reader has a few snatch of collage physics.

Traffic and Random Processes: An Introduction

This e-book bargains in a simple and systematic demeanour with the basics of random functionality thought and appears at a few elements regarding arrival, motor vehicle headway and operational pace strategies even as. The paintings serves as an invaluable sensible and academic software and goals at supplying stimulus and motivation to enquire problems with the sort of powerful applicative curiosity.

Additional info for Gibbs Measures on Cayley Trees

Example text

Download PDF sample

Rated 4.10 of 5 – based on 46 votes