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1.

図書
図書
1. Gibbs random fields : cluster expansions
by V.A. Malyshev and R.A. Minlos
出版情報: Dordrecht [Netherlands] ; Boston : Kluwer Academic Publishers, c1991  xiv, 248 p. ; 25 cm
シリーズ名: Mathematics and its applications ; . Soviet series ; v. 44
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2.

図書
図書
2. Linear infinite-particle operators
V.A. Malyshev, R.A. Minlos
出版情報: Providence, R.I. : American Mathematical Society, c1995  viii, 298 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 143
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目次情報: 続きを見る
Introduction
Extended introduction
Construction of a nonequilibrium dynamics
Construction of an equilibrium dynamics
Spectral analysis of the Euclidean field transfer matrix
Asymptotic completeness for interacting fermion systems
The method of Bethe-Salpeter kernels (Dyson's equation)
Guide to the Literature
References
Introduction
Extended introduction
Construction of a nonequilibrium dynamics
3.

図書
図書
3. Topics in the constructive theory of countable Markov chains (: hardback)
G. Fayolle, V.A. Malyshev, M.V. Menshikov
出版情報: Cambridge [England] : Cambridge University Press, 1995  169 p. ; 24 cm
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Introduction and history
Preliminaries / 1：
General criteria / 2：
Explicit construction of Lyapunov functions / 3：
Ideology of induced chains / 4：
Random walks in two dimensional complexes / 5：
Stability / 6：
Exponential convergence and analyticity for ergodic Markov chains / 7：
Bibliography
Introduction and history
Preliminaries / 1：
General criteria / 2：
4.

図書
図書
4. Asymptotic combinatorics with application to mathematical physics
edited by Vadim Malyshev and Anatoly Vershik
出版情報: Dordrecht : Kluwer Academic, c2002  xv, 327 p. ; 25 cm
シリーズ名: NATO science series ; Sub-series II . Mathematics, physics and chemistry ; v. 77
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Preface
Program
List of participants
Matrix Models and Graph Enumeration / Part 1：
Matrix Quantum Mechanics / V. Kazakov
Introduction to matrix models / E. Brezin
A Class of the Multi-Interval Eigenvalue Distributions of Matrix Models and Related Structures / V. Buslaev ; L. Pastur
Combinatorics and Probability of Maps / V. A. Malyshev
The Combinatorics of Alternating Tangles: from theory to computerized enumeration / J. L. Jacobsen ; P. Zinn-Justin
Invariance Principles for Non-uniform Random Mappings and Trees / D. Aldous ; J. Pitman
Integrable Models (of Statistical Physics and Quantum Field Theory) / Part 2：
Renormalization group solution of fermionic Dyson model / M. D. Missarov
Statistical Mechanics and Number Theory / H. E. Boos ; V. E. Korepin
Quantization of Thermodynamics and the Bardeen-Cooper-Schriffer-Bogolyubov Equation / V. P. Maslov
Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2D / D. S. Grebenkov
Representation Theory / Part 3：
Notes on homogeneous vector bundles over complex flag manifolds / S. Igonin
Representations Theory and Doubles of Yangians of Classical Lie Superalgebras / V. Stukopin
Idempotent (asymptotic) Mathematics and the Representation theory / G. L. Litvinov ; G. B. Shpiz
A new approach to Berezin kernels and canonical representations / G. van Dijk
Theta Hypergeometric Series / V. P. Spiridonov
Preface
Program
List of participants
5.

図書
図書
5. Random walks in the quarter-plane : algebraic methods, boundary value problems and applications (: hardcover)
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
出版情報: Berlin ; New York : Springer, c1999  xv, 156 p. ; 25 cm
シリーズ名: Applications of mathematics ; 40
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目次情報: 続きを見る
Introduction and History
Probabilistic Background / 1：
Markov Chains / 1.1：
Random Walks in a Quarter Plane / 1.2：
Functional Equations for the Invariant Measure / 1.3：
Foundations of the Analytic Approach / 2：
Fundamental Notions and Definitions / 2.1：
Covering Manifolds / 2.1.1：
Algebraic Functions / 2.1.2：
Elements of Galois Theory / 2.1.3：
Universal Cover and Uniformization / 2.1.4：
Abelian Differentials and Divisors / 2.1.5：
Restricting the Equation to an Algebraic Curve / 2.2：
First Insight (Algebraic Functions) / 2.2.1：
Second Insight (Algebraic Curve) / 2.2.2：
Third Insight (Factorization) / 2.2.3：
Fourth Insight (Riemann Surfaces) / 2.2.4：
The Algebraic Curve Q(x,y) = 0 / 2.3：
Branches of the Algebraic Functions on the Unit Circle / 2.3.1：
Branch Points / 2.3.2：
Galois Automorphisms and the Group of the Random Walk / 2.4：
? and ? on S / 2.4.1：
Reduction of the Main Equation to the Riemann Torus / 2.5：
Analytic Continuation of the Unknown Functions in the Genus Case / 3：
Lifting the Fundamental Equation onto the Universal Covering / 3.1：
Lifting of the Branch Points / 3.1.1：
Lifting of the Automorphisms on the Universal Covering / 3.1.2：
Analytic Continuation / 3.2：
More about Uniformization / 3.3：
The Case of a Finite Group / 4：
On the Conditions for H to be Finite / 4.1：
Explicit Conditions for Groups of Order 4 or 6 / 4.1.1：
The General Case / 4.1.2：
Rational Solutions / 4.2：
The Case N(f) = 1 / 4.2.1：
Algebraic Solutions / 4.2.2：
Final Form of the General Solution / 4.3.1：
The Problem of the Poles and Examples / 4.5：
Reversible Random Walks / 4.5.1：
Simple Examples of Nonreversible Random Walks / 4.5.1.2：
One Parameter Families / 4.5.1.3：
Two Typical Situations / 4.5.1.4：
Ergodicity Conditions / 4.5.1.5：
Proof of Lemma 4.5.2 / 4.5.1.6：
An Example of Algebraic Solution by Flatto and Hahn / 4.6：
Two Queues in Tandem / 4.7：
Solution in the Case of an Arbitrary Group / 5：
Informal Reduction to a Riemann-Hilbert-Carleman BVP / 5.1：
Introduction to BVP in the Complex Plane / 5.2：
A Bit of History / 5.2.1：
The Sokhotski-Plemelj Formulae / 5.2.2：
The Riemann Boundary Value Problem for a Closed Con- tour / 5.2.3：
The Riemann BVP for an Open Contour / 5.2.4：
The Riemann-Carleman Problem with a Shift / 5.2.5：
Further Properties of the Branches Defined by Q(x,y) = 0 / 5.3：
Index and Solution of the BVP (5.1.5) / 5.4：
Complements / 5.5：
Computation of w / 5.5.1：
An Explicit Form via the Weierstrass P-Function / 5.5.2.1：
A Differential Equation / 5.5.2.2：
An Integral Equation / 5.5.2.3：
The Genus 0 Case / 6：
Properties of the Branches / 6.1：
Case 1: <$$$> / 6.2：
Case 3: <$$$> / 6.3：
Case 4: <$$$> / 6.4：
Integral Equation / 6.4.1：
Series Representation / 6.4.2：
Uniformization / 6.4.3：
Boundary Value Problem / 6.4.4：
Case 5: <$$$> / 6.5：
Miscellanea / 7：
About Explicit Solutions / 7.1：
Asymptotics / 7.2：
Large Deviations and Stationary Probabilities / 7.2.1：
Generalized Problems and Analytic Continuation / 7.3：
Outside Probability / 7.4：
References
Index
Introduction and History
Probabilistic Background / 1：
Markov Chains / 1.1：
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