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1.

図書

図書
Harry Kesten
出版情報: Boston : Birkhäuser, 1982  423 p. ; 24 cm
シリーズ名: Progress in probability and statistics ; v. 2
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2.

図書

図書
Kesten, Harry, 1931-
出版情報: Providence, R.I. : American Mathematical Society, 1969  129 p. ; 26 cm
シリーズ名: Memoirs of the American Mathematical Society ; no. 93
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3.

図書

図書
Maury Bramson, Rick Durrett, editors
出版情報: Boston : Birkhauser, c1999  x, 398 p. ; 25 cm
シリーズ名: Progress in probability / series editors, Thomas Liggett, Charles Newman, Loren Pitt ; 44
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4.

図書

図書
Harry Kesten, editor
出版情報: New York ; Tokyo : Springer-Verlag, c1987  xi, 323 p. ; 25 cm
シリーズ名: The IMA volumes in mathematics and its applications ; v. 8
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5.

図書

図書
R. Carmona, H. Kesten, J.B. Walsh ; édite par P.L. Hennequin
出版情報: Berlin ; Tokyo : Springer-Verlag, c1986  x, 439 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1180
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6.

図書

図書
Rick Durrett, Harry Kesten, editors
出版情報: Boston : Birkhäuser, 1991  ix, 455 p. ; 24 cm
シリーズ名: Progress in probability ; 28
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7.

図書

図書
Joel E. Cohen, Harry Kesten, and Charles M. Newman, editors
出版情報: Providence, R.I. : American Mathematical Society, c1986  xiv, 358 p. ; 26 cm
シリーズ名: Contemporary mathematics ; v. 50
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目次情報: 続きを見る
Limit theorems for products of random matrices / J. C. Watkins
Oseledec's multiplicative ergodic theorem / J. Cohen ; H. Kesten ; C. M. Newman
Products of random matrices: convergence theorems / Y. Guivarch ; A. Raugi
Examples of application of Oseledec's theorem / F. Ledrappier
Multiplicative ergodic theorems for random diffeomorphisms / Y. Kifer
Furstenberg-Kesten results: asymptotic analysis / S. Pincus
Stability of exponential growth rate for randomly perturbed random matrix products via Markov-chain arguments / E. V. Slud
Representation, positivity, and expansion of Lyapunov exponents for linear stochastic systems / V. Wihstutz
On uniform contraction generated by positive matrices / M. Wojtkowski
Lyapunov exponents for some products of random matrices
A brief survey on the spectral radius and the spectral distribution of large random matrices with i.i.d. entries / V.-R. Hwang
Eigenvalues and eigenvectors of large dimensional sample covariance matrices / J. W. Silverstein
Spectra for large dimensional random matrices / Y. Q. Yin ; Z. D. Bai
Products of random matrices and computer image generation / P. Diaconis ; M. Shahshahani
Products of random matrices as they arise in the study of random walks on groups
On products of random stochastic matrices / R. Cogburn
Convolution sequences of measures on the semigroup of stochastic matrices / M. Rosenblatt
Random walks on semigroups / T.-C. Sun
A note on random systems with complete connections and their applications to products of random matrices / T.Kaijser
Using random matrices to give recurrence and transience criteria for random walk in a random environment / E. Key
A contraction principle for certain Markov chains and its application / G. Letac
Lyapunov exponents and spectra for one-dimensional random Schroedinger operators / S. Kotani
The density of states of random Schroedinger operators / R. S. Maier
Random matrices in nuclear physics and number theory / M. L. Mehta
Random matrices and waves in random media / G. Papanicolaou
Demographic applications of random matrix products / S. Tuljapurkar
Limit theorems for products of random matrices / J. C. Watkins
Oseledec's multiplicative ergodic theorem / J. Cohen ; H. Kesten ; C. M. Newman
Products of random matrices: convergence theorems / Y. Guivarch ; A. Raugi
8.

図書

図書
Harry Kesten (editor)
出版情報: Berlin ; Tokyo : Springer, c2004  vi, 351 p. ; 25 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 110 . Probability theory ; 1
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目次情報: 続きを見る
The Random-Cluster Model / Geoffrey Grimmett
Models of First-Passage Percolation / C. Douglas Howard
Relaxation Times of Markov Chains in Statistical Mechanics and Combinatorial Structures / Fabio Martinelli
Random Walks on Finite Groups / Laurent Saloff-Coste
Index
Introduction / 1:
A Motivating Example: the Assignment Problem / 1.1:
A Stalking Horse: the Partial Matching Problem / 1.2:
Organization of the Survey / 1.3:
Geometric Graphs and Local Weak Convergence / 2:
Geometric Graphs / 2.1:
<$>{\cal G}^\ast<$> as a Metric Space / 2.2:
Local Weak Convergence / 2.3:
The Standard Construction / 2.4:
A Prototype: The Limit of Uniform Random Trees / 2.5:
Maximal Weight Partial Matching on Random Trees / 3:
Weighted Matchings of Graphs in General / 3.1:
Our Case: Random Trees with Random Edge Weights / 3.2:
Two Obvious Guesses: One Right, One Wrong / 3.3:
Not Your Grandfather's Recursion / 3.4:
A Direct and Intuitive Plan / 3.5:
Characterization of the Limit of <$>B(T_n^{small})<$> / 3.6:
Characterization of the Limit of <$>B(T_n^{big})<$> / 3.7:
The Limit Theorem for Maximum Weight Partial Matchings / 3.8:
Closing the Loop: Another Probabilistic Solution of a Fixed-Point Equation / 3.9:
From Coupling to Stability - Thence to Convergence / 3.10:
Looking Back: Perspective on a Case Study / 3.11:
The Mean-Field Model of Distance / 4:
From Poisson Points in <$>{\op R}^{d}<$> to a Simple Distance Model / 4.1:
The Poisson Weighted Infinite Tree - or, the PWIT / 4.2:
The Cut-off Components of a Weighted Graph and a PWIT / 4.3:
The Minimum Spanning Forests of an Infinite Graph / 4.4:
The Average Length Per Vertex of the MSF of a PWIT / 4.5:
The Connection to Frieze's ζ(3) Theorem / 4.6:
Minimal Cost Perfect Matchings / 5:
A Natural Heuristic - Which Fails for a Good Reason / 5.1:
Involution Invariance and the Standard Construction / 5.2:
Involution Invariance and the Convergence of MSTs / 5.3:
A Heuristic That Works by Focusing on the Unknown / 5.4:
A Distributional Identity with a Logistic Solution / 5.5:
A Stochastic Process that Constructs a Matching / 5.6:
Calculation of a Limiting Constant: <$>\pi^{2}/6<$> / 5.7:
Passage from a PWIT Matching to a Kn Matching / 5.8:
Finally - Living Beyond One's Means / 5.9:
Problems in Euclidean Space / 6:
A Motivating Problem / 6.1:
Far Away Places and Their Influence / 6.2:
Euclidean Methods and Some Observations in Passing / 6.3:
Recurrence of Random Walks in Limits of Planar Graphs / 6.4:
Limitations, Challenges, and Perspectives / 7:
References
Potts and random-cluster processes
Random-cluster measures
Ising and Potts models
Random-cluster and Ising-Potts coupled
The limit as <$>q \downarrow 0<$>
Rank-generating functions
Infinite-volume random-cluster measures
Stochastic ordering
A differential formula
Conditional probabilities
Infinite-volume weak limits
Random-cluster measures on infinite graphs
The case q < 1
Phase transition, the big picture
Infinite open clusters
First- and second-order phase transition
General results in d (≥ 2) dimensions
The subcritical phase, p < pc(q)
The supercritical phase, p > pc(q)
Near the critical point, p ≃ pc(q)
In two dimensions
Graphical duality
Value of the critical point
First-order phase transition
SLE limit when q ≤ 4
On complete graphs and trees
On complete graphs / 7.1:
On trees and non-amenable graphs / 7.2:
Time-evolutions of random-cluster models / 8:
Reversible dynamics / 8.1:
Coupling from the past / 8.2:
Swendsen-Wang dynamics / 8.3:
The Basic Model and Some Fundamental Questions
Notation
The Time Constant
The Fundamental Processes of Hammersley and Welsh
About μ
Minimizing Paths
Asymptotic Shape and Shape Fluctuations
Shape Theorems for Standard FPP
About the Asymptotic Shape for Lattice FPP
FPP Based on Poisson Point Processes
Upper Bounds on Shape Fluctuations
Some Related Longitudinal Fluctuation Exponents
Monotonicity
Transversal Fluctuations and the Divergence of Shape Fluctuations
Transversal Fluctuation Exponents
Upper Bounds on <$>\xi<$>
Lower Bounds on <$>\chi<$>
Lower Bounds on <$>\xi<$>
Fluctuations for Other Related Models
Infinite Geodesics and Spanning Trees
Semi-Infinite Geodesics and Spanning Trees
Coalescence and Another Spanning Tree in 2 Dimensions
Doubly-Infinite Geodesics
Summary of Some Open Problems
Mixing times for reversible, continuous-time Markov chains
Analytic methods
Tensorization of the Poincaré and logarithmic Sobolev inequalities
Geometric tools
Comparison methods
Coupling methods and block dynamics
Statistical mechanics models in <$>{\op Z}^d<$>
Grand canonical Gibbs measures
Mixing conditions and absence of long-range order
Canonical Gibbs measures for lattice gases
The ferromagnetic Ising and Potts models
FK representation of Potts models
Antiferromagnetic models on an arbitrary graph: Potts and hard-core models
Model with random interactions
Unbounded spin systems
Ground states of certain quantum Heisenberg models as classical Gibbs measures
Glauber dynamics in <$>{\op Z}^d<$>
The dynamics in a finite volume
The dynamics in an infinite volume
Graphical construction
Uniform ergodicity and logarithmic Sobolev constant
Mixing property versus logarithmic Sobolev constant in <$>{\op Z}^d<$>
The auxiliary chain and sweeping out relations method
The renormalization group approach
The martingale method
The recursive analysis
Rapid mixing for unbounded spin systems
Torpid mixing in the phase coexistence region
Torpid mixing for the Ising model in <$>\Lambda \subset {\op Z}^{d}<$> with free boundary conditions
Interface driven mixing inside one phase
Torpid mixing for Potts model in <$>{\op Z}^d<$>
Glauber dynamics for certain random systems in <$>{\op Z}^d<$>
Combination of torpid and rapid mixing: the dilute Ising model
Relaxation to equilibrium for spin glasses
Glauber dynamics for more general structures
Glauber dynamics on trees and hyperbolic graphs
Glauber dynamics for the hard-core model
Cluster algorithms: the Swendsen-Wang dynamics for Potts models
Mixing time for conservative dynamics / 9:
Random transposition, Bernoulli-Laplace and symmetric simple exclusion / 9.1:
The asymmetric simple exclusion / 9.2:
The Kac model for the Boltzmann equation / 9.3:
Adsorbing staircase walks / 9.4:
Kawasaki dynamics for lattice gases / 10:
Diffusive scaling of the mixing time in the one-phase region / 10.1:
Background and Notation / 10.2:
Finite Markov Chains
Invariant Markov Chains on Finite Groups
Shuffling Cards and the Cut-off Phenomenon
Three Examples of Card Shuffling
Exact Computations
The Cut-off Phenomenon
Probabilistic Methods
Coupling
Strong Stationary Times
Spectrum and Singular Values
General Finite Markov Chains
The Random Walk Case
Lower Bounds
Eigenvalue Bounds Using Paths
Cayley Graphs
The Second Largest Eigenvalue
The Lowest Eigenvalue
Diameter Bounds, Isoperimetry and Expanders
Results Involving Volume Growth Conditions
Moderate Growth
Nilpotent Groups
Nilpotent Groups with many Generators / 7.3:
Representation Theory for Finite Groups
The General Set-up
Abelian Examples
Random Random Walks
Central Measures and Bi-invariant Walks
Characters and Bi-invariance
Random Transposition on the Symmetric Group
Walks Based on Conjugacy Classes of the Symmetric Group
Finite Classical Groups
Fourier Analysis for Non-central Measures / 9.5:
Comparison Techniques
The min-max Characterization of Eigenvalues
Comparing Dirichlet Forms Using Paths
Comparison for Non-symmetric Walks / 10.3:
The Random-Cluster Model / Geoffrey Grimmett
Models of First-Passage Percolation / C. Douglas Howard
Relaxation Times of Markov Chains in Statistical Mechanics and Combinatorial Structures / Fabio Martinelli
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