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

Buch | Hardcover
X, 246 Seiten
2012 | 2012
Springer Basel (Verlag)
978-3-0348-0355-7 (ISBN)

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Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions - Lev A. Sakhnovich
90,94 inkl. MwSt
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.
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.

Introduction.- 1 Levy processes.- 2 The principle of imperceptibility of the boundary.- 3 Approximation of positive functions.- 4 Optimal prediction and matched filtering.- 5 Effective construction of a class of non-factorable operators.- 6 Comparison of thermodynamic characteristics.- 7 Dual canonical systems and dual matrix string equations.- 8 Integrable operators and Canonical Differential Systems.- 9 The game between energy and entropy.- 10 Inhomogeneous Boltzmann equations.- 11 Operator Bezoutiant and concrete examples.- Comments.- Bibliography.- Glossary.- Index.

Erscheint lt. Verlag 18.7.2012
Reihe/Serie Operator Theory: Advances and Applications
Zusatzinfo X, 246 p.
Verlagsort Basel
Sprache englisch
Maße 155 x 235 mm
Gewicht 525 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Graphentheorie
Schlagworte combinatorics • Energy • Entropy • Levy processes • stable processes • triangular factorization • Wahrscheinlichkeitsrechnung
ISBN-10 3-0348-0355-9 / 3034803559
ISBN-13 978-3-0348-0355-7 / 9783034803557
Zustand Neuware
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