Introduction to Random Matrices

ISBN-10: 0521194520

ISBN-13: 9780521194525

Edition: 2009

List price: $135.00 Buy it from $85.93
This item qualifies for FREE shipping

*A minimum purchase of $35 is required. Shipping is provided via FedEx SmartPost® and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace" orders are not eligible for free or discounted shipping.

30 day, 100% satisfaction guarantee

If an item you ordered from TextbookRush does not meet your expectations due to an error on our part, simply fill out a return request and then return it by mail within 30 days of ordering it for a full refund of item cost.

Learn more about our returns policy

Description:

New Starting from $85.93
what's this?
Rush Rewards U
Members Receive:
coins
coins
You have reached 400 XP and carrot coins. That is the daily max!
Study Briefs

Limited time offer: Get the first one free! (?)

All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.

Add to cart
Study Briefs
Calculus 1 Online content $4.95 $1.99
Add to cart
Study Briefs
Algebra Online content $4.95 $1.99
Add to cart
Study Briefs
Introduction to Logic Online content $4.95 $1.99
Add to cart
Study Briefs
Business Math Formulas Online content $4.95 $1.99
Customers also bought
Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading
Loading

Book details

List price: $135.00
Copyright year: 2009
Publisher: Cambridge University Press
Publication date: 11/19/2009
Binding: Hardcover
Pages: 506
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 1.848
Language: English

Preface
Introduction
Real and complex Wigner matrices
Real Wigner matrices: traces, moments and combinatorics
The semicircle distribution, Catalan numbers and Dyck paths
Proof #1 of Wigner's Theorem 2.1.1
Proof of Lemma 2.1.6: words and graphs
Proof of Lemma 2.1.7: sentences and graphs
Some useful approximations
Maximal eigenvalues and F�redi-Koml�s enumeration
Central limit theorems for moments
Complex Wigner matrices
Concentration for functionals of random matrices and logarithmic Sobolev inequalities
Smoothness properties of linear functions of the empirical measure
Concentration inequalities for independent variables satisfying logarithmic Sobolev inequalities
Concentration for Wigner-type matrices
Stieltjes transforms and recursions
Gaussian Wigner matrices
General Wigner matrices
Joint distribution of eigenvalues in the GOE and the GUE
Definition and preliminary discussion of the GOE and the GUE
Proof of the joint distribution of eigenvalues
Selberg's integral formula and proof of (2.5.4)
Joint distribution of eigenvalues: alternative formulation
Superposition and decimation relations
Large deviations for random matrices
Large deviations for the empirical measure
Large deviations for the top eigenvalue
Bibliographical notes
Hermite polynomials, spacings and limit distributions for the Gaussian ensembles
Summary of main results: spacing distributions in the bulk and edge of the spectrum for the Gaussian ensembles
Limit results for the GUE
Generalizations: limit formulas for the GOE and GSE
Hermite polynomials and the GUE
The GUE and determinantal laws
Properties of the Hermite polynomials and oscillator wave-functions
The semicircle law revisited
Calculation of moments of L<sub>N</sub>
The Harer-Zagier recursion and Ledoux's argument
Quick introduction to Fredholm determinants
The setting, fundamental estimates and definition of the Fredholm determinant
Definition of the Fredholm adjugant, Fredholm resolvent and a fundamental identity
Gap probabilities at 0 and proof of Theorem 3.1.1
The method of Laplace
Evaluation of the scaling limit: proof of Lemma 3.5.1
A complement: determinantal relations
Analysis of the sine-kernel
General differentiation formulas
Derivation of the differential equations: proof of Theorem 3.6.1
Reduction to Painlev� V
Edge-scaling: proof of Theorem 3.1.4
Vague convergence of the largest eigenvalue: proof of Theorem 3.1.4
Steepest descent: proof of Lemma 3.7.2
Properties of the Airy functions and proof of Lemma 3.7.1
Analysis of the Tracy-Widom distribution and proof of Theorem 3.1.5
The first standard moves of the game
The wrinkle in the carpet
Linkage to Painlev� II
Limiting behavior of the GOE and the GSE
Pfaffians and gap probabilities
Fredholm representation of gap probabilities
Limit calculations
Differential equations
Bibliographical notes
Some generalities
Joint distribution of eigenvalues in the classical matrix ensembles
Integration formulas for classical ensembles
Manifolds, volume measures and the coarea formula
An integration formula of Weyl type
Applications of Weyl's formula
Determinantal point processes
Point processes: basic definitions
Determinantal processes
Determinantal projections
The CLT for determinantal processes
Determinantal processes associated with eigenvalues
Translation invariant determinantal processes
One-dimensional translation invariant determinantal processes
Convergence issues
Examples
Stochastic analysis for random matrices
Dyson's Brownian motion
A dynamical version of Wigner's Theorem
Dynamical central limit theorems
Large deviation bounds
Concentration of measure and random matrices
Concentration inequalities for Hermitian matrices with independent entries
Concentration inequalities for matrices with dependent entries
Tridiagonal matrix models and the � ensembles
Tridiagonal representation of � ensembles
Scaling limits at the edge of the spectrum
Bibliographical notes
Free probability
Introduction and main results
Noncommutative laws and noncommutative probability spaces
Algebraic noncommutative probability spaces and laws
C*-probability spaces and the weak*-topology
W*-probability spaces
Free independence
Independence and free independence
Free independence and combinatorics
Consequence of free independence: free convolution
Free central limit theorem
Freeness for unbounded variables
Link with random matrices
Convergence of the operator norm of polynomials of independent GUE matrices
Bibliographical notes
Appendices
Linear algebra preliminaries
Identities and bounds
Perturbations for normal and Hermitian matrices
Noncommutative matrix L<sup>p</sup>-norms
Brief review of resultants and discriminants
Topological preliminaries
Generalities
Topological vector spaces and weak topologies
Banach and Polish spaces
Some elements of analysis
Probability measures on Polish spaces
Generalities
Weak topology
Basic notions of large deviations
The skew field H of quaternions and matrix theory over F
Matrix terminology over F and factorization theorems
The spectral theorem and key corollaries
A specialized result on projectors
Algebra for curvature computations
Manifolds
Manifolds embedded in Euclidean space
Proof of the coarea formula
Metrics, connections, curvature, Hessians, and the Laplace-Beltrami operator
Appendix on operator algebras
Basic definitions
Spectral properties
States and positivity
von Neumann algebras
Noncommutative functional calculus
Stochastic calculus notions
References
General conventions and notation
Index
×
Free shipping on orders over $35*

*A minimum purchase of $35 is required. Shipping is provided via FedEx SmartPost® and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace" orders are not eligible for free or discounted shipping.

Learn more about the TextbookRush Marketplace.

×