Course on “Free Probability Theory”, winter term 2018/19

  • the lectures are videotaped, the recordings can be found here
  • for blog entries related to this class check this link.

handwritten lecture notes

  • Section 0: (very short) introduction into subject and history
  • Section 1: The notion of freeness: definition, example, basic properties
  • Section 2: The emergence of the combinatorics of FPT: free (central) limit theorem
  • Section 3: The combinatorics of FPT: free cumulants
  • Section 4: Free convolution of compactly supported probability measures and the R-transform
  • Section 5: Free convolution of arbitrary probability measures and the subordination function
  • Section 6: Gaussian random matrices and asymptotic freeness
  • Section 7: Unitary random matrices and asymptotic freeness
  • computer slides from the end of Section 7: Random matrices and free convolution
  • Section 8: von Neumann algebras: the free group factors and relation to freeness
  • Section 9: Circular and R-diagonal operators
  • Section 10: Applications of freeness to vN algebras: compression of free group factors
  • Section 11: Some more operator algebraic applications of free probability