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1.

図書

図書
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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目次情報: 続きを見る
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
2.

図書

図書
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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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:
3.

図書

図書
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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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
4.

図書

図書
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:
5.

図書

図書
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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