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Kihoon Seong (KAIST): Gibbs measures with log-correlated Gaussian fields and its invariance under Hamiltonian PDEs

Ort: MPI für Mathematik in den Naturwissenschaften Leipzig, Videobroadcast

Vortrag in der Reihe: Arbeitsgemeinschaft ANGEWANDTE ANALYSIS We study the Gibbs measure with log-correlated base Gaussian fields on the d-dimensional torus. When d = 2, the Gibbs measure corresponds to the well-studied Phi^k_2-measure. We first discuss the (non-)construction of the focusing Gibbs measure. As a Hamiltonian PDE system corresponding to the Gibbs measure, we consider the Zakharov-Yukawa system (Schr¨odinger-wave system with a Zakharov-type coupling) on the two-dimensional torus. We then present a phase transition and invariance of the Gibbs measure under the flow. This is based on joint work with Tadahiro Oh (University of Edinburgh) and Leonardo Tolomeo (University of Bonn).

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Beginn: Jan. 17, 2022, 1 p.m.

Ende: Jan. 17, 2022, 2:30 p.m.