Título: Random walk on the simple symmetric exclusion process
Palestrante: Daniel Kious
Data: : 31/03/2021
Horario: 13:00h
Local: Transmissão online
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Resumo: In a joint work with Marcelo R. Hilário and Augusto Teixeira, we investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium. At each jump, the random walker is subject to a drift that depends on whether it is sitting on top of a particle or a hole. The asymptotic behavior is expected to depend on the density ρ in [0, 1] of the underlying SSEP. Our first result is a law of large numbers (LLN) for the random walker for all densities ρ except for at most two values ρ− and ρ+ in [0, 1], where the speed (as a function fo the density) possibly jumps from, or to, 0. Second, we prove that, for any density corresponding to a non-zero speed regime, the fluctuations are diffusive and a Central Limit Theorem holds. Our main results extend to environments given by a family of independent simple symmetric random walks in equilibrium
ID da reunião: 958 0581 3232
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: 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: 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.
