The Partition Method for a Power Series Expansion, Kowalenko, Victor

Автор: Su Zhonggen
Название: Random Matrices And Random Partitions: Normal Convergence
ISBN: 9814612227 ISBN-13(EAN): 9789814612227
Издательство: World Scientific Publishing
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Описание: This Book Is Aimed At Graduate Students And Researchers Who Are Interested In The Probability Limit Theory Of Random Matrices And Random Partitions. It Mainly Consists Of Three Parts. Part I Is A Brief Review Of Classical Central Limit Theorems For Sums Of Independent Random Variables, Martingale Sequences And Markov Chains, Etc. These Classical Theorems Are Frequently Used In The Study Of Random Matrices And Random Partitions Where Random Matrices Are Well-Studied In Probability Theory. Part Ii Concentrates On The Asymptotic Distribution Theory Of Circular Unitary Ensemble And Gaussian Unitary Ensemble, Which Are Prototypes Of Random Matrix Theory. It Turns Out That The Classical Central Limit Theorems And Methods Are Applicable In Describing Asymptotic Distributions Of Eigenvalue Statistics Like Linear Functionals Of Eigenvalues. This Is Attributed To The Nice Algebraic Structures Of Models. This Part Also Studies The Circular β Ensembles And Gaussian β Ensembles, Which May Be Viewed As Extensions Of The Circular Unitary Ensemble And Gaussian Unitary Ensemble. Part Iii Is Devoted To The Study Of Random Uniform And Plancherel Partitions. As Is Known, There Is A Surprising Similarity Between Random Matrices And Random Integer Partitions From The Viewpoint Of Asymptotic Distribution Theory, Though It Is Difficult To Find Any Direct Link Between The Two Finite Models.This Book Treats Only Second-Order Fluctuations For Primary Random Variables From Two Classes Of Special Random Models. It Is Written In A Clear, Concise And Pedagogical Way. It May Be Read As An Introductory Text To Further Study Probability Theory Of General Random Matrices, Random Partitions And Even Random Point Processes. This Book Is Aimed At Graduate Students And Researchers Who Are Interested In Probability Limit Theory Of Random Matrices And Random Integer Partitions.

Автор: Borot
Название: Asymptotic Expansion of a Partition Function Related to the Sinh-model
ISBN: 331933378X ISBN-13(EAN): 9783319333786
Издательство: Springer
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Описание: This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.