Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions

Lev A. Sakhnovich

ISBN 10: 3034803559 / ISBN 13: 9783034803557

Edité par Springer Basel, Birkhäuser Basel Jul 2012, 2012

A propos de cet article

Neuware -In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac's problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson's theorem, Ringrose's hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us to investigate the special classes of the entire functions.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 256 pp. Englisch.

N° de réf. du vendeur 9783034803557

Détails bibliographiques

• Titre: Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions
• Éditeur: Springer Basel, Birkhäuser Basel Jul 2012
• Date de parution: 2012
• Langue: anglais
• ISBN à 10 chiffres: 3034803559
• ISBN à 13 chiffres: 9783034803557
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 19 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 19 millimètres de profondeur
• Poids: 553 grammes

A propos de ce titre

Synopsis

In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac's problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson's theorem, Ringrose's hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us to investigate the special classes of the entire functions.

Présentation de l'éditeur

This book explores the interconnection of probability and analysis, in an approach mainly based on the application of analysis methods to probability theory. Among many concepts, the authors address problems of statistical physics from the game point of view.