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14 06 im noticia Gaussian free field on a cylinderTítulo: Lozenge tilings and the Gaussian free field on a cylinder

Palestrante: Marianna Russkikh, MIT
Data: 16/06/2021
Horário: 13:00h
Local: Transmissão online.

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ID da reunião: 958 0581 3232

Resumo: We discuss new results on lozenge tilings on an infinite cylinder, which may be analyzed using the periodic Schur process introduced by Borodin. Under one variant of the $q^{vol}$ measure, corresponding to random cylindric partitions, the height function converges to a deterministic limit shape and fluctuations around it are given by the Gaussian free field in the conformal structure predicted by the Kenyon-Okounkov conjecture. Under another variant, corresponding to an unrestricted tiling model on the cylinder, the fluctuations are given by the same Gaussian free field with an additional discrete Gaussian shift component. Fluctuations of the latter type have been previously conjectured by Gorin for tiling models on planar domains with holes. This talk is based on joint work with Andrew Ahn and Roger Van Peski.

08 06 im noticia Kirchhoff forests and Markov spectraTítulo: Kirchhoff forests and Markov spectra

Palestrante: Alexandre Gaudillière (Université Aix Marseille)
Data: 14/06/2021
Horário: 15:00hrs a 16:00hrs
Local: Transmissão online

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Resumo: Wilson's algorithm efficiently samples spanning forests of a given network that are associated with a partition function that coincides, in accordance with a theorem by Kirchhoff, with the characteristic polynomial of the infinitesimal generator of the continuous time random walk on the network. This provides a probabilistic proof of this theorem and we will discuss how it also gives access to various Markov spectrum properties and estimates.

Acesse AQUI as gravações dos seminários online de 2020.

Este ano, alguns dias depois da reunião, os vídeos devem estar disponíveis AQUI.

Todas as palestras são ministradas em inglês.

01 06 im noticia SeminárioProbabilidadeTítulo: Kahane's Gaussian Multiplicative Chaos and Circular Random Matrices match exactly.

Palestrante: Reda Chhaibbi, University Paul Sabatier, Toulouse
Data: 02/06/2021.
Horário: 13:00h
Local: Transmissão online.

Confira AQUI o link para transmissão.
ID da reunião: 958 0581 3232

Resumo: In this talk, I would like to advertise the strict equality between two objects from very different areas of mathematical physics: - Kahane's Gaussian Multiplicative Chaos (GMC), which uses a log-correlated field as input and plays an important role in certain conformal field theories - A reference model in random matrices called the Circular Beta Ensemble (CBE). The goal is to give a precise theorem whose loose form is GMC = CBE. Although it was known that random matrices exhibit log-correlated features, such an exact correspondence is quite a surprise.

07 06 im noticia Using KirchhoffsTítulo: Using Kirchhoff's forests for network immunisation

Palestrante: Alexandre Gaudillière, Université Aix-Marseille
Data: 09/06/2021
Horário: 13:00h
Local: Transmissão online.

Confira AQUI o link para transmissão.
ID da reunião: 958 0581 3232

Resumo: We will discuss how one can use Kirchhoff's random spanning forests to choose which nodes to immunize, or remove, inside a given network in order to make it more resistant from a simple mathematical point of view on epidemic propagations. This is a joint work with Irina Gurewitsch, Luca Avena and Michael Emmerich.

31 05 im noticia SeminarioProbabilidadeTítulo: Fast mixing time for the exclusion process in a random environment

Palestrante: Hubert Lacoin (IMPA)
Data: 07/06/2021
Horário: 15:00hrs
Local: Transmissão online

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Resumo: We consider a system of $k$ particles on a segment of size $N$. Its rules of evolution are the following: a particle at site $x \in \{1 ,\dots, N\}$ jumps to $x+1$ with rate $\omega_x$ and to $x-1$ with rate $1-\omega_x$ where $\omega_x\in (0,1)$, and a jump is cancelled if the site is already occupied. We consider the case where $(\omega_x)^N_{x=1}$ is (the fixed realization of) a sequence of IID random variables. Assuming that $\mathbb E[ \log\frac{1-\omega_x}{\omega_x}]\ne 0$ (that is, transience of the random environment), we prove that this particle systems mixes fast, in the sense that the time that it requires for its distribution to get close to the equilibrium state grows like a power of $N$. We present a lower bound for the power in mixing time which we conjecture to be sharp. Joint work with S. Yang, IMPA.

Acesse AQUI as gravações dos seminários online de 2020.

Este ano, alguns dias depois da reunião, os vídeos devem estar disponíveis AQUI.

Todas as palestras são ministradas em inglês.

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