Random Matrix Theory and Its Applications - Lecture 5
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
Recap - Rot inv ensembles Gaussian
Two approaches - finite N approach
Large N continuum approach
What is the typical scale of lambda?
Large N - coarse graining
Step 1: Introduce an empirical density
Step 2: Coarse graining - Partial tracing
Saddle point method
Finite support of the charged density
Cauchy singular value equation
F.G. Tricomi, 1957
Famous Wigner semi-circular law
Scale of interparticle distance
Asymptotic properties
Tracy & Widom, 1994
Taught by
International Centre for Theoretical Sciences