Ruprecht-Karls-Universität Heidelberg
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Informationen für
„Gemeinsames Mathematik-Physik Kolloquium“
Universality for Random Matrices and Log-Gases
Prof. László Erdős, IST Austria, Klosterneuburg

Eugene Wigner's revolutionary vision predicted that the energy levels of large complex quantum systems exhibit a universal behavior: the statistics of energy gaps depend only on the basic symmetry type of the model. These universal statistics show strong correlations in the form of level repulsion and they seem to represent a new paradigm of point processes that are characteristically different from the Poisson statistics of independent points. Simplified models of Wigner's thesis have recently become mathematically accessible. For mean field models represented by large random matrices with independent entries, the celebrated Wigner-Dyson-Gaudin-Mehta (WDGM) conjecture asserts that the local eigenvalue statistics are universal. For invariant matrix models, the eigenvalue distributions are given by a log-gas with potential V and inverse temperature ß= 1, 2, 4. For ß∉ {1, 2, 4}, there is no natural random matrix ensemble behind this model, but the analogue of the WDGM conjecture asserts that the local statistics are independent of $V$. In this lecture I explain the main ideas leading to the recent solution of these conjectures.

Donnerstag, den 10. Juli 2014 um 17 Uhr c.t. Uhr, in INF 288, HS2 Donnerstag, den 10. Juli 2014 at 17 Uhr c.t., in INF 288, HS2

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. M. Salmhofer