Gibbs Measures On Cayley Trees

DOWNLOAD

Download Gibbs Measures On Cayley Trees PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Gibbs Measures On Cayley Trees book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Gibbs Measures On Cayley Trees

DOWNLOAD
Author : Utkir A. Rozikov
language : en
Publisher: World Scientific
Release Date : 2013

Gibbs Measures On Cayley Trees written by Utkir A. Rozikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.

The 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. The 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.

Gibbs Measures In Biology And Physics The Potts Model

DOWNLOAD
Author : Utkir A Rozikov
language : en
Publisher: World Scientific
Release Date : 2022-07-28

Gibbs Measures In Biology And Physics The Potts Model written by Utkir A Rozikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-28 with Mathematics categories.

This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.

Gibbs Measures And Phase Transitions

DOWNLOAD
Author : Hans-Otto Georgii
language : en
Publisher: Walter de Gruyter
Release Date : 2011-05-31

Gibbs Measures And Phase Transitions written by Hans-Otto Georgii and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-31 with Mathematics categories.

"This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.

Geometric Formulation Of Classical And Quantum Mechanics

DOWNLOAD
Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 2011

Geometric Formulation Of Classical And Quantum Mechanics written by G. Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.

The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.

On The Emergence Theme Of Physics

DOWNLOAD
Author : Robert Carroll
language : en
Publisher: World Scientific
Release Date : 2010

On The Emergence Theme Of Physics written by Robert Carroll and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

The book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great detail. Some original work relating the quantum potential and Ricci flow is also included.

Combinatorial Stochastic Processes

DOWNLOAD
Author : Jim Pitman
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-11

Combinatorial Stochastic Processes written by Jim Pitman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-11 with Mathematics categories.

The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

Advances In Non Archimedean Analysis And Applications

DOWNLOAD
Author : W. A. Zúñiga-Galindo
language : en
Publisher: Springer Nature
Release Date : 2021-12-02

Advances In Non Archimedean Analysis And Applications written by W. A. Zúñiga-Galindo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-02 with Mathematics categories.

This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications. Featuring new techniques developed by leading experts in the field, it highlights the relevance and depth of this important area of mathematics, in particular its expanding reach into the physical, biological, social, and computational sciences as well as engineering and technology. In the last forty years the connections between non-Archimedean mathematics and disciplines such as physics, biology, economics and engineering, have received considerable attention. Ultrametric spaces appear naturally in models where hierarchy plays a central role – a phenomenon known as ultrametricity. In the 80s, the idea of using ultrametric spaces to describe the states of complex systems, with a natural hierarchical structure, emerged in the works of Fraunfelder, Parisi, Stein and others. A central paradigm in the physics of certain complex systems – for instance, proteins – asserts that the dynamics of such a system can be modeled as a random walk on the energy landscape of the system. To construct mathematical models, the energy landscape is approximated by an ultrametric space (a finite rooted tree), and then the dynamics of the system is modeled as a random walk on the leaves of a finite tree. In the same decade, Volovich proposed using ultrametric spaces in physical models dealing with very short distances. This conjecture has led to a large body of research in quantum field theory and string theory. In economics, the non-Archimedean utility theory uses probability measures with values in ordered non-Archimedean fields. Ultrametric spaces are also vital in classification and clustering techniques. Currently, researchers are actively investigating the following areas: p-adic dynamical systems, p-adic techniques in cryptography, p-adic reaction-diffusion equations and biological models, p-adic models in geophysics, stochastic processes in ultrametric spaces, applications of ultrametric spaces in data processing, and more. This contributed volume gathers the latest theoretical developments as well as state-of-the art applications of non-Archimedean analysis. It covers non-Archimedean and non-commutative geometry, renormalization, p-adic quantum field theory and p-adic quantum mechanics, as well as p-adic string theory and p-adic dynamics. Further topics include ultrametric bioinformation, cryptography and bioinformatics in p-adic settings, non-Archimedean spacetime, gravity and cosmology, p-adic methods in spin glasses, and non-Archimedean analysis of mental spaces. By doing so, it highlights new avenues of research in the mathematical sciences, biosciences and computational sciences.

Advanced Classical Field Theory

DOWNLOAD
Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 2009

Advanced Classical Field Theory written by G. Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Science categories.

Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories OCo gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory OCo are presented in a complete way. This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained.

Proceedings Of The International Conference On Mathematical Sciences And Statistics 2022 Icmss 2022

DOWNLOAD
Author : Nadihah Wahi
language : en
Publisher: Springer Nature
Release Date : 2023-02-10

Proceedings Of The International Conference On Mathematical Sciences And Statistics 2022 Icmss 2022 written by Nadihah Wahi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-10 with Mathematics categories.

This is an open access book. The ICMSS2022 is an international conference jointly organised by the Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia together with the Banasthali University, Jaipur, India. This international conference aims to give exposure and to bring together academicians, researchers and industry experts for intellectual growth. The ICMSS2022 serves as a platform for the scientific community members to exchange ideas and approaches, to present research findings, and to discuss current issues and topics related to mathematics, statistics as well as their applications. Objectives: to present the most recent discoveries in mathematics and statistics. to serve as a platform for knowledge and information sharing between experts from industries and academia. to identify and create potential collaboration among participants. The organising committee of ICMSS2022 welcomes all delegates to deliberate over various aspects related to the conference themes and sub-themes.

Information Physics And Computation

DOWNLOAD
Author : Marc Mézard
language : en
Publisher: Oxford University Press
Release Date : 2009-01-22

Information Physics And Computation written by Marc Mézard and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-22 with Computers categories.

A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.