### From a formula of Haagerup to random matrices and free probability

- Series
- Analysis Seminar
- Time
- Wednesday, November 14, 2012 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Ionel Popescu – Georgia Tech – ipopescu@math.gatech.edu

This formula of Haagerup gives an expression of the log|x-y| in terms of
Chebyshev polynomials of the first kind. This is very useful for
problems involving the logarithmic potentials which plays a prominent
role in random matrices, free probability, orthogonal polynomials and
other areas. We will show how one can go from this to several things,
for example the counting problems of planar diagrams and functional
inequalities in free probability in particular an intriguing Poincare
inequality and some related other inequalities. If time allows I will
also talk about a conjecture related to the Hilbert transform,
semicircular and arcsine distribution. Parts of this was with Stavros
Garoufalidis and some other parts with Michel Ledoux.