Linear Systems and Differential Equations in Random Matrix Theory
Schmid College, Chapman University via YouTube
Overview
Syllabus
Intro
Plan
Controllability and observability operators
Evolution of the linear system
Howland operators via linear systems
Theta and tau functions
Classical tau functions and PDE
Linear system for solving the sinh-Gordon equation
Scattering functions
Solving the coupled ODE
Matrix potentials
The bracket operation
Potentials and derivatives
Solution of the coupled ODE
Matrix potential in Gelfand-Levitan equation
Hankel determinant for deformed Laguerre weight
Painleve III' equations
Random matrix model
Equilibrium potential
Free logarithmic Sobolev inequality
Taught by
Schmid College, Chapman University