Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Leonid Pastur
Mathematical Division, Institute for Low Temperatures, Kharkiv, Ukraine
Fluctuation laws of spectral statistics for large random matrices
We consider certain functions of eigenvalues and eigenvectors (spectral statistics) of real symmetric and
hermitian random matrices of large size. We first show that for these functions an analog of the Law
of Large Numbers is valid as the size of matrices tends to infinity. We then discuss the scale and the
form for limiting fluctuations laws of the statistics and show that the laws can be standard Gaussian (i.e.,
analogous to usual Central Limit Theorem for appropriately normalized sums of i.i.d. random variables) in
non-standard asymptotic settings, certain non-Gaussian in seemingly standard asymptotic settings, and
other non-Gaussian in non-standard asymptotic settings.
Manfred Salmhofer
Universität Heidelberg
Renormalization group analysis of Fermi systems with pointlike singularities
We consider the quantum field theoretical description of quantum many-body systems. In fermionic gases
at low densities, and in specific materials of solid-state physics, the Fermi surface becomes small or
even degenerates to a point. A multiscale analysis can be used to determine the correlation functions by
convergent expansions. In the talk I will discuss models for double-layer graphene and the dilute Fermi
gas, and explain the main ideas in the analysis.
Benjamin Schlein
Hausdorff-Zentrum für Mathematik, Bonn
The average density of states of hermitian Wigner matrices
In this talk we will consider the density of states (DOS) of Wigner matrices on very small intervals. In such
intervals, the fluctuations of the DOS are important and one cannot expect convergence to the semicircle
law to hold in probability. Assuming the entries of the matrices to have a sufficiently regular law, we prove,
nevertheless, that the average DOS still converges to the semicircle law, on arbitrarily small intervals.
Christoph Schweigert
Fachbereich Mathematik, Universität Hamburg und Zentrum für mathematische Physik
Higher categories in field theory - an invitation
We explain the notation of a bicategory and its use in topological, classical and quantum field theory.
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