Random Matrix Theory and Its Applications - Lecture 3
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
Recap: Random matrices with real spectrum
Complex quaternionic matrices
Other examples of rotationally invariant ensembles
Exercise: 2x2 - generic orthonormal transit
Specific orthonormal transit
Joint distribution of eigenvalues
Trick - Right set of variables to change
Remarks
Rotational Invariant Ensemble
3x3 - Gaussian case
Counting degrees of fraction
Special property of rotationally invariant ensembles
Real symmetric rotationally invariant ensemble
Complex Hermitian Case
Complex Quaternionic
For rotationally Invariant ensemble =eigenvalues & eigenvectors decouple
1 d disordered model - GOE and Anderson model
Taught by
International Centre for Theoretical Sciences