Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions PDF Download
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Author: Lev A. Sakhnovich
Publisher: Springer Science & Business Media
ISBN: 3034803567
Category : Mathematics
Languages : en
Pages : 246
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Book Description
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.
Author: Lev A. Sakhnovich
Publisher: Springer Science & Business Media
ISBN: 3034803567
Category : Mathematics
Languages : en
Pages : 246
Get Book Here
Book Description
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.
Author: Springer
Publisher:
ISBN: 9783034803571
Category :
Languages : en
Pages : 258
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Book Description
Author: Daniel Alpay
Publisher: Birkhäuser
ISBN: 3319103350
Category : Mathematics
Languages : en
Pages : 396
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Book Description
The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich's research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.
Author: Alexander L. Sakhnovich
Publisher: Walter de Gruyter
ISBN: 3110258617
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.
Author: Serena Dipierro
Publisher: Springer
ISBN: 303018921X
Category : Mathematics
Languages : en
Pages : 502
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Book Description
This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.
Author: Michael Plischke
Publisher: World Scientific
ISBN: 9789810216429
Category : Science
Languages : en
Pages : 540
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Book Description
This textbook concentrates on modern topics in statistical physics with an emphasis on strongly interacting condensed matter systems. The book is self-contained and is suitable for beginning graduate students in physics and materials science or undergraduates who have taken an introductory course in statistical mechanics. Phase transitions and critical phenomena are discussed in detail including mean field and Landau theories and the renormalization group approach. The theories are applied to a number of interesting systems such as magnets, liquid crystals, polymers, membranes, interacting Bose and Fermi fluids; disordered systems, percolation and spin of equilibrium concepts are also discussed. Computer simulations of condensed matter systems by Monte Carlo-based and molecular dynamics methods are treated.
Author: Roberto Livi
Publisher: Cambridge University Press
ISBN: 1107049547
Category : Science
Languages : en
Pages : 439
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Book Description
A comprehensive and pedagogical text on nonequilibrium statistical physics, covering topics from random walks to pattern formation.
Author: David P. Landau
Publisher: Cambridge University Press
ISBN: 9780521653664
Category : Mathematics
Languages : en
Pages : 402
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Book Description
This book describes all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, as well as in related fields, such as polymer science and lattice gauge theory. The authors give a succinct overview of simple sampling methods and develop the importance sampling method. In addition they introduce quantum Monte Carlo methods, aspects of simulations of growth phenomena and other systems far from equilibrium, and the Monte Carlo Renormalization Group approach to critical phenomena. The book includes many applications, examples, and current references, and exercises to help the reader.
Author: Rosario N. Mantegna
Publisher: Cambridge University Press
ISBN: 1139431226
Category : Business & Economics
Languages : en
Pages : 164
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Book Description
This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.
Author: Oliver Knill
Publisher: World Scientific Publishing Company
ISBN: 9789813109490
Category : Mathematics
Languages : en
Pages : 500
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Book Description
This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.
