Título: Using Kirchhoff's forests for network immunisation

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

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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.

Título: 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.

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Título: 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.

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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.

Título: Facilitated Exclusion Processes

Palestrante: Eugene Speer, Rutgers University
Data: 26/05/2021
Horário: 13:00h
Local: Transmissão online

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ID da reunião: 958 0581 3232

Resumo: Facilitated exclusion processes are lattice gasses in which a particle with an empty neighboring site can jump to that site only if it has also an occupied neighboring site. We will discuss three such models in one dimension, for both discrete-time and continuous-time dynamics and with varying degrees of asymmetry. We address two questions: What are the possible translation invariant stationary states? If the initial state is Bernoulli, what is the final state? This is joint work with Arvind Ayyer, Shelly Goldstein, and Joel Lebowitz.