Título: Condensation of SIP particles and sticky Brownian motio

Palestrante: Gioia Carinci, University of Modena and R. Emilia.
Data: 14/04/2021
Horario: 14:00h
Local: Transmissão online.

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ID da reunião: 958 0581 3232

Resumo: The symmetric inclusion process (SIP) is a particle system with attractive interaction. We study its behavior in the condensation regime attained for large values of the attraction intensity. Using Mosco convergence of Dirichlet forms, we prove convergence to sticky Brownian motion for the distance of two SIP particles. We use this result to obtain, via duality, an explicit scaling for the variance of the density field in this regime, for the SIP initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing particle systems on the infinite lattice. Joint work with M. Ayala and F. Redig.

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: Gravitational allocation of uniform points on the sphere

Palestrante: Yuval Peres (Kent State University)
Data: 12/04/2021
Horário: 15:00h
Local: Transmissão online

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Resumo: Given uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them? "Fairly" means that each region has the same area. It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins of attraction for the resulting gradient flow yield such a partition-with exactly equal areas, no matter how the points are distributed. This is related to work of Nazarov-Sodin-Volberg on Gaussian analytic functions. (See the cover of the AMS Notices at http://www.ams.org/publications/journals/notices/201705/rnoti-cvr1.pdf.) Our main result is that this partition minimizes, up to a bounded factor, the average distance between points in the same cell. I will also present an application to almost optimal matching on the sphere, connecting to a classical result of Ajtai, Komlos and Tusnady (Combinatorica 1984).

Joint work with Nina Holden and Alex Zhai.

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.