Lamé Seminar on "Mathematical Physics and Disordered
Organizers: Frédéric Klopp
(), Alexander Fedotov
V.A. Steklov Mathematical Institute
(St.-Petersburg, Fontanka 27)
May 28th, 2014, 17:00, room 203
T. Shcherbina (Chebyshev Lab, St.Petersburg),
Title: Universality of the local regime for some types of random band matrices.
In this talk we will discuss an application of the supersymmetric
method (SUSY) to the analysis of the bulk local regime for some types
of random band matrices (RBM). SUSY approach is widely used in the
physics literature and is potentially very powerful but the rigorous
control of the integral representations, which can be obtained by this
method, is difficult and so far for RBM it has been performed only for
the density of states. Here we present some rigorous SUSY results
about the universality of the second correlation function of the
Gaussian block RBM.
April 23rd, 2014, 17:00, room 203
D. Chelkak (PDMI RAS & Chebyshev Lab, St.Petersburg),
Title: Magnetization in the `layered' Ising model and truncated
determinants of square roots of Jacobi matrices.
Abstract: In this talk we present a new explicit formula for the magnetization
(average value of a particular spin) in the layered Ising model in a
half-plane (above, 'layered' means that interaction constants depend on the
distance to the boundary only). The answer is given in terms of truncated
determinants of the square root of a simple Jacobi matrix constructed from
a sequence of interaction constants. The proof is based on a new direct
link between spin expectations in the planar Ising model and the theory of
orthogonal polynomials via Smirnov's fermionic observable. This is a joint
work with Clement Hongler (New York).
May 21st, 2014, 17:00, room 203
D. Zaporozhets (PDMI RAS & Chebyshev Lab, St.Petersburg),
Title: Asymptotic behavior of zeros of random polynomials and analytic functions
Abstract: here it is.