Título: Lattice trees in high dimensions
Palestrante: Manuel Cabezas (Universidad Católica de Chile, Santiago)
Data: 29/03/2021
Horário: 15h - 16h
Local: Transmissão online
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Resumo: Lattice trees is a probabilistic model for random subtrees of \Z^d. In this talk we are going to review some previous results about the convergence of lattice trees to the "Super-Brownian motion" in the high-dimensional setting. Then, we are going to show some new theorems which strengthen the topology of said convergence. Finally, if time permits, we will discuss the applications of these results to the study of random walks on lattice trees.
Joint work with A. Fribergh, M. Holmes and E. Perkins.
Título: A hard rod system with non homogeneous sizes
Palestrante: Pablo A Ferrari, Universidad de Buenos Aires
Data: 24/03/2021
Horário: 14:00h
Local: Transmissão online.
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Resumo: A rod (q,v,d) represents a segment (q,q+d) travelling at speed v, in absence of other rods. The hard rod condition means that rods cannot intersect. When two rods collide, they immediately swap positions so that the slower rod stays to the left. This model, introduced by Boldrighini, Dobrushin and Sukhov in 1982, has infinitely many conservation laws, a feature shared by the Generalized Gibbs Ensemble. I will present work in progress for the case of variable d, including a characterization of the invariant measures, and a generalized hydrodynamic limit. Work in collaboration with Dante Grevino.
ID da reunião: 958 0581 3232
Título: Scaling limits of uniform spanning trees in three dimensions
Palestrante: Saraí Hernández-Torres
Data: 17/03/2021
Horário: 15:00 até 16:00.
Local: Transmissão online.
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Resumo:
The uniform spanning tree (UST) on Z^3 is the infinite-volume limit of uniformly chosen spanning trees of large finite subgraphs of Z^3. The main result in this talk is the existence of subsequential scaling limits of the UST on Z^3. Furthermore, we have convergence over a particular subsequence. An essential tool is Wilson’s algorithm which samples uniform spanning trees by using loop-erased random walks (LERW). This talk will focus on the properties of the three-dimensional LERW crucial in our proofs. This is joint work with Omer Angel, David Croydon, and Daisuke Shiraishi.
Título: Limiting shape for some random processes on groups of polynomial growth
Palestrante: Lucas Roberto de Lima (UFABC)
Data: 22/03/2021
Horário: 15:00h
Local: Transmissão online.
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Resumo:
We study conditions for the existence of the asymptotic shape for subadditive processes defined on Cayley graphs of finitely generated groups with polynomial growth. We will focus our attention on the cases of First-Passage Percolation and the Frog Model. The considered class of graphs is an algebraic generalization of the hypercubic Z^d lattice, and the related limiting shape results combine probability with techniques from geometric group theory. This talk is based on a joint work with Cristian Coletti
Título: Exact solution of an integrable particle system.
Autor: Cristian Giardina, University of Modena
Data: 17/03/2021
Horário: 14:00h
Local: Transmissão online.
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ID da reunião: 958 0581 3232
Resumo:
We consider the family of boundary-driven models introduced in [FGK] and show they can be solved exactly, i.e. the correlations functions and the non-equilibrium steady-state have a closed-form expression. The solution relies on probabilistic arguments and techniques inspired by integrable systems. As in the context of bulk-driven systems (scaling to KPZ), it is obtained in two steps: i) the introduction of a dual process; ii) the solution of the dual dynamics by Bethe ansatz. For boundary-driven systems, a general by-product of duality is the existence of a direct mapping (a conjugation) between the generator of the non-equilibrium process and the generator of the associated reversible equilibrium process. Macroscopically, this mapping was observed years ago by Tailleur, Kurchan and Lecomte in the context of the Macroscopic Fluctuation Theory.
[FGK] R. Frassek, C. Giardinà, J. Kurchan, Non-compact quantum spin chains as integrable stochastic particle processes, Journal of Statistical Physics 180, 366-397 (2020).
