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Author:   Makoto Katori
Publisher:   Springer Verlag, Singapore
Imprint:   Springer Verlag, Singapore
Edition:   1st ed. 2016
Volume:   11
Dimensions:   Width: 15.50cm , Height: 0.80cm , Length: 23.50cm
Weight:   2.409kg
ISBN:  

9789811002748

ISBN 10:   9811002746
Pages:   141
Publication Date:   16 February 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

1 Bessel Process1.1 One-Dimensional BrownianMotion (BM) 1.2 Martingale Polynomials of BM 1.3 Drift Transform 1.4 Quadratic Variation 1.5 Stochastic Integration 1.6 Ito's Formula 1.7 Complex Brownian Motion and Conformal Invariance 1.8 Stochastic Differential Equation for Bessel Process 1.9 Kolmogorov Equation 1.10 BES(3) and Absorbing BM1.11 BES(1) and Reflecting BM 1.12 Critical Dimension Dc = 2 1.13 Bessel Flow and Another Critical Dimension Dc = 3/2 1.14 Hypergeometric Functions Representing Bessel Flow Exercises References 2 Schramm--Loewner Evolution (SLE) 2.1 Complexification of Bessel Flow2.2 Schwarz--Christoffel Formula and Loewner Chain 2.3 Three Phases of SLE2.4 Cardy's Formula 2.5 SLE and Statistical Mechanics Models Exercises References 3 Dyson Model 3.1 Multivariate Extension of Bessel Process 3.2 DysonModel as Eigenvalue Process 3.3 Dyson Model as Noncolliding Brownian Motion 3.4 Determinantal Martingale Representation (DMR) 3.5 Reducibility of DMR and Correlation Functions 3.5.1 Density Function rx(t, x) 3.5.2 Two-Time Correlation Function rx (s, x;t, y) 3.6 Determinantal Process 3.7 Constant-Drift Transform of Dyson Model 3.8 Generalization for Initial Configuration with Multiple Points 3.9 Wigner's Semicircle Law and Scaling Limits 3.9.1 Wigner's Semicircle Law3.9.2 Bulk Scaling Limit and Homogeneous Infinite System <3.9.3 Soft-Edge Scaling Limit and Spatially Inhomogeneous Infinite System3.10 Entire Functions and Infinite Particle Systems 3.10.1 Nonequilibrium Sine Process 3.10.2 Nonequilibrium Airy Process 3.11 Tracy--Widom Distribution 3.11.1 Distribution Function of Maximum Position of Particles 3.11.2 Algebraic Calculation 3.11.3 System of Differential Equations 3.11.4 Nonlinear Third-Order Differential Equation 3.11.5 Soft-Edge Scaling Limit 3.11.6 Painleve II and Limit Theorem of Tracy and Widom 3.12 Beyond Determinantal Processes Exercises References Solutions Index

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