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Lecture Topic : (Pure Math) RANDOM MATRICES (M2, Mehta)

Prerequisites : Linear Algebra (Jun, Sen); Analytic Number Theory (Sen, M1); Abstract Algebra (Sen); Abstract Algebra (M1); Nuclear Physics (M1); Statistical Theory (Sen, M1);

Recommended Text(s) :

“Random Matrices”, 3rd Edn., Madan Lal Mehta, Elsevier, 2004.

Approx price new on (hard copy) : $105

Approx price second hand on (hard copy) : $75

Availability free on (e-format) : Yes

eMule search key word(s) : Random Matrices, Mehta

Lectures and Links :


Lecture 1  (link)

Ch.1   Introduction

Ch.2   Gaussian Ensembles : The Joint Probability Density Function for the Matrix Elements

Ch.3   Gaussian Ensembles : The Joint Probability Density Function for the Eigenvalues


Lecture 2  (link)

Ch.4   Gaussian Ensembles Level Density

Ch.5   Orthogonal, Skew-Orthogonal and Bi-Orthogonal Polynomials

Ch.6   Gaussian Unitary Ensemble


Lecture 3  (link)

Ch.7   Gaussian Orthogonal Ensemble

Ch.8   Gaussian Symplectic Ensemble

Ch.9   Gaussian Ensembles : Brownian Motion Model


Lecture 4  (link)

Ch.10  Circular Ensembles

Ch.11  Circular Ensembles (continued)

Ch.12  Circular Ensembles : Thermodynamics


Lecture 5  (link)

Ch.13   Gaussian Ensemble of Anti-Symmetric Hermitian Matrices

Ch.14   A Gaussian Ensemble of Hermitian Matrices with Unequal Real and Imaginary Parts

Ch.15   Matrices with Gaussian Element Densities but with no Unitary or Hermitian Conditions Imposed.


Lecture 6  (link)

Ch.16   Statistical Analysis of a Level-Sequence

Ch.17   Selberg’s Integral and Its Consequences

Ch.18   Asymptotic Behavior of Eb(0,s) by Inverse Scattering


Lecture 7  (link)

Ch.19   Matrix Ensembles and Classical Orthogonal Polynomials

Ch.20   Level Spacing Functions Eb(r,s) : Inter-Relations and Power Series Expansions

Ch.21   Fredholm Determinants and Painleve Equations


Lecture 8  (link)

Ch.22   Moments of the Characteristic Polynomial in the Three Ensembles of Random Matrices

Ch.23   Hermitian Matrices Coupled in a Chain

Ch.24   Gaussian Ensembles : Edge of the Spectrum


Lecture 9  (link)

Ch.25   Random Permutations, Circular Unitary Ensemble (CUE) and Gaussian Unitary Ensemble (GUE)

Ch.26   Probability Densities of the Determinants; Gaussian Ensembles

Ch.27   Restricted Trace Ensembles


Links to Other Lecturers on this Topic :

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