Linear Systems and Differential Equations in Random Matrix Theory

Linear Systems and Differential Equations in Random Matrix Theory

Schmid College, Chapman University via YouTube Direct link

Plan

2 of 20

2 of 20

Plan

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Classroom Contents

Linear Systems and Differential Equations in Random Matrix Theory

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

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