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Classroom Contents
Linear Systems and Differential Equations in Random Matrix Theory
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- 1 Intro
- 2 Plan
- 3 Controllability and observability operators
- 4 Evolution of the linear system
- 5 Howland operators via linear systems
- 6 Theta and tau functions
- 7 Classical tau functions and PDE
- 8 Linear system for solving the sinh-Gordon equation
- 9 Scattering functions
- 10 Solving the coupled ODE
- 11 Matrix potentials
- 12 The bracket operation
- 13 Potentials and derivatives
- 14 Solution of the coupled ODE
- 15 Matrix potential in Gelfand-Levitan equation
- 16 Hankel determinant for deformed Laguerre weight
- 17 Painleve III' equations
- 18 Random matrix model
- 19 Equilibrium potential
- 20 Free logarithmic Sobolev inequality
