Sarah-Jean Meyer, Univ. Oxford: The FBSDE approach to sine-Gordon up to 6? (Oberseminar Mathematische Stochastik)
Wednesday, 10.04.2024 16:00 im Raum SRZ 204
I will present a stochastic analysis of the sine-Gordon Euclidean quantum field (cos(? ?))_2 on the full space up to the second threshold, i.e. for ?^2<6*?. The basis of our method is a stochastic quantisation equation given by a forward-backward stochastic differential equation (FBSDE) for a decomposition (X_t)_(t?0) of the interacting Euclidean field X_? along a scale parameter t?0 using an approximate version of the renormalisation flow equation. The FBSDE produces a scale-by-scale coupling of the interacting field with the Gaussian free field without cut-offs and describes the optimiser of a stochastic control problem for Euclidean QFTs introduced by Barashkov and Gubinelli. I will first explain the general set-up for the FBSDE approach. In the case of the sine-Gordon model, I will showcase some applications of the FBSDE to illustrate that it can be used effectively to obtain results about large deviations, integrability, decay of correlations for local observables, singularity with respect to the free field, Osterwalder-Schrader axioms and other properties. This is joint work with Massimiliano Gubinelli.
Angelegt am Monday, 29.01.2024 15:44 von Anita Kollwitz
Geändert am Monday, 18.03.2024 13:34 von Frank Wübbeling
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Wilhelm Killing Kolloquium: Prof. Dr. Antti Knowles (University of Geneva): Random graphs as models of quantum disorder
Thursday, 11.04.2024 14:15 im Raum M4
A disordered quantum system is mathematically described by a large Hermitian random matrix. One of the most remarkable phenomena expected to occur in such systems is a localization-delocalization transition for the eigenvectors. Originally proposed in the 1950s to model conduction in semiconductors with random impurities, this phenomenon is now recognized as a general feature of wave transport in disordered media, and is one of the most influential ideas in modern condensed matter physics. A simple and natural model of a disordered quantum system is given by the adjacency matrix of a random graph. I report on recent progress in analysing the phase diagram for the Erdös-Renyi model of random graphs. In particular, I explain the emergence of fully localized and fully delocalized phases, which are separated by a mobility edge. Joint work with Johannes Alt and Raphael Ducatez.
Angelegt am Wednesday, 07.02.2024 10:57 von Claudia Lückert
Geändert am Tuesday, 05.03.2024 15:28 von Claudia Lückert
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