- Series
- Stochastics Seminar
- Time
- Thursday, April 18, 2013 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skyles 006
- Speaker
- Paul Bourgade – Harvard University
- Organizer
- Karim Lounici
Wigner stated the general hypothesis that the distribution of
eigenvalue spacings of large complicated quantum systems is universal in
the sense that it depends only on the symmetry class of the physical system
but not on other detailed structures. The simplest case for this hypothesis
concerns large but finite dimensional matrices. Spectacular progress was
done in the past two decades to prove universality of random matrices
presenting an orthogonal, unitary or symplectic invariance. These models
correspond to log-gases with respective inverse temperature 1, 2 or 4. I
will report on a joint work with L. Erdos and H.-T. Yau, which yields
universality for log-gases at arbitrary temperature at the microscopic
scale. A main step consists in the optimal localization of the particles,
and the involved techniques include a multiscale analysis and a local
logarithmic Sobolev inequality.