Statistical analysis and universal limit theorems in the theory of random matrices

Prof. Kenneth McLaughlin

Number of cycles: 1

Second semester


  1. Introduction to random matrices.
    • First example: Gaussian Random matrices, symmetric case.
    • Numerical experimentation.
    • Definitions of the basic quantities of study.
    • Homework: exact evaluation in the case N=2, proving various pieces of the puzzle.
    • Second example: Gaussian Random Matrices, self-adjoint case.
    • Numerical experimentation.
    • Homework: numerical simulations.
    • Third example: Wishart random matrices of various kinds
    • Numerical experimentation.
  2. Asymptotic analysis for N large.
    • Exact formulae for N finite.
    • Homework: evaluation of some exact statistical quantities.
    • Summary of asymptotic results.
    • Summary of methods employed for these results.
    • The sound and the fury of asymptotic analysis: the case of Hermite polynomials.
    • Homework: asymptotic analysis canon
  3. A few statistical applications (presentations by students).
  4. Limit Theorems!.
  5. Recent results and open directions for research.