Media Storage Type : DVD-ROM
NPTEL Course Name : Random Matrix Theory and Applications
NPTEL Subject Matter Expert : Dr. Pragya Shukla
NPTEL Co-ordinating Institute : IIT Kharagpur
NPTEL Lecture Count : 40
Lecture Titles:
Lecture 1 - Complexity in physical systems: various forms
Lecture 2 - Statistical behavior of physical properties
Lecture 3 - Need of random matrix models
Lecture 4 - Probability and information entropy
Lecture 5 - Natural probability measure: the role of symmetries
Lecture 6 - The maximum entropy criterion in the context of statistical inferences
Lecture 7 - Nature of ensemble: Role of symmetry, interactions and other system conditions: Part - I
Lecture 8 - Nature of ensemble: Role of symmetry, interactions and other system conditions: Part - II
Lecture 9 - Nature of ensemble: Role of symmetry, interactions and other system conditions: Part - III
Lecture 10 - Basis invariance vs Basis dependence of the ensemble: Part - I
Lecture 11 - Basis invariance vs Basis dependence of the ensemble: Part - II
Lecture 12 - Invariant Gaussian ensembles of Hermitian matrices: Wigner-Dyson ensembles (general)
Lecture 13 - Invariant Gaussian ensembles of Hermitian matrices: eigenvalues-distribution of 2 2 Wigner-Dyson ensembles
Lecture 14 - Invariant Gaussian ensembles of Hermitian matrices: eigenvalues/ eigenfunctions distributions of N X N Wigner-Dyson ensembles
Lecture 15 - Invariant Gaussian ensembles of Hermitian matrices: Chiral ensembles
Lecture 16 - Invariant Gaussian ensembles of Hermitian matrices: particle-hole ensembles
Lecture 17 - Time-periodic systems and circular ensembles of unitary matrices
Lecture 18 - Non-Hermitian, Laguerre ensembles
Lecture 19 - Level Density
Lecture 20 - Fluctuation measures of eigenvalues: basics
Lecture 21 - 2nd order level correlations
Lecture 22 - Higher order fluctuation measures
Lecture 23 - Fluctuation measures of eigenfunctions
Lecture 24 - Fluctuation measures of eigenfunctions (Continued...)
Lecture 25 - Multifractality, Universality etc
Lecture 26 - Varying system conditions and transition between stationary ensembles
Lecture 27 - Common mathematical formulation of eigenvalue statistics
Lecture 28 - Common mathematical formulation of uctuation measures: Examples
Lecture 29 - Connection to one dimensional Calogero-Sutherland Hamiltonian
Lecture 30 - Correlated random matrix ensembles: common mathematical formulation of eigenvalues statistics
Lecture 31 - Critical ensembles and role of complexity parameter
Lecture 32 - Random matrix theory of quantum transport
Lecture 33 - Quantum Chaos and Random matrix theory
Lecture 34 - Disordered Systems and Random matrix theory
Lecture 35 - Many body physics, eld theories and Random matrix theory
Lecture 36 - Financial and Atmospheric uctuations
Lecture 37 - Complex Networks
Lecture 38 - Biological Systems
Lecture 39 - Application to classical and quantum optics
Lecture 40 - Waves in solid, liquids and number-theory