A Course on Large Deviations with an Introduction to Gibbs Measures - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course on Large Deviations with an Introduction to Gibbs Measures write by Firas Rassoul-Agha. This book was released on 2015-03-12. A Course on Large Deviations with an Introduction to Gibbs Measures available in PDF, EPUB and Kindle. This is an introductory course on the methods of computing asymptotics of probabilities of rare events: the theory of large deviations. The book combines large deviation theory with basic statistical mechanics, namely Gibbs measures with their variational characterization and the phase transition of the Ising model, in a text intended for a one semester or quarter course. The book begins with a straightforward approach to the key ideas and results of large deviation theory in the context of independent identically distributed random variables. This includes Cramér's theorem, relative entropy, Sanov's theorem, process level large deviations, convex duality, and change of measure arguments. Dependence is introduced through the interactions potentials of equilibrium statistical mechanics. The phase transition of the Ising model is proved in two different ways: first in the classical way with the Peierls argument, Dobrushin's uniqueness condition, and correlation inequalities and then a second time through the percolation approach. Beyond the large deviations of independent variables and Gibbs measures, later parts of the book treat large deviations of Markov chains, the Gärtner-Ellis theorem, and a large deviation theorem of Baxter and Jain that is then applied to a nonstationary process and a random walk in a dynamical random environment. The book has been used with students from mathematics, statistics, engineering, and the sciences and has been written for a broad audience with advanced technical training. Appendixes review basic material from analysis and probability theory and also prove some of the technical results used in the text.
Large Deviations for the Empirical Field of Gibbs Measure
Large Deviations for the Empirical Field of Gibbs Measure - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Large Deviations for the Empirical Field of Gibbs Measure write by University of Minnesota. Institute for Mathematics and Its Applications. This book was released on 1986. Large Deviations for the Empirical Field of Gibbs Measure available in PDF, EPUB and Kindle.
Gibbs Measures and Phase Transitions
Gibbs Measures and Phase Transitions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Gibbs Measures and Phase Transitions write by Hans-Otto Georgii. This book was released on 2011. Gibbs Measures and Phase Transitions available in PDF, EPUB and Kindle. From a review of the first edition: "This book [...] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. [...] 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." (F. Papangelou
Large Deviation for Weak Gibbs Measures and Multifractal Spectra
Large Deviation for Weak Gibbs Measures and Multifractal Spectra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Large Deviation for Weak Gibbs Measures and Multifractal Spectra write by Marc Keßeböhmer. This book was released on 2000. Large Deviation for Weak Gibbs Measures and Multifractal Spectra available in PDF, EPUB and Kindle.
Gibbs Measures On Cayley Trees
Gibbs Measures On Cayley Trees - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Gibbs Measures On Cayley Trees write by Utkir A Rozikov. This book was released on 2013-07-11. Gibbs Measures On Cayley Trees available in PDF, EPUB and Kindle. The purpose of this book is to present systematically all known mathematical results on Gibbs measures on Cayley trees (Bethe lattices).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.
