Random Matrix Theory and its Applications - Lecture 4
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
Recap - Rotationally invariant ensemble
1. Focus on Rotation Invariant Ensemble Gaussian Case
Joint Distribution - Gibbs -Boltzmann prob
Ising model
Distribution of the matrix entries
Exercise
Natural observables
2. n-point correlation function
3. Spacing distribution bet n neighbouring eigenvalues
Wigner surmise
4. Counting Statistics
For Gaussian ensembles
Extreme value statistics of correlated random variables
R. M. May Nature, 238, 413 1972 - "Will a large complex system be stable"?
Switch on pairwise interaction
Stable
Taught by
International Centre for Theoretical Sciences