Palestra: A zero range process with rapidly growing rates
Palestrante: Enrique D. Andjel (Aix Marseille)
Data: 24 de junho de 2019 (segunda-feira)
Hora: 15:30 h
Local: B106-a – Bloco B - CT – Instituto de Matemática - UFRJ
Resumo: Most constructions of the zero range process assume that the rate at which a particle leaves a site grows at most linearly with the number of particles present at that site. We provide a method to construct a zero range processes with super-linear rates on $\mathbb{Z}^d $ when either the initial distribution is translation invariant or d=1 and only nearest neighbor jumps are allowed.
Palestra: On the singularity of random symmetric matrices
Palestrante: Letícia Mattos (IMPA)
Data: 13 de maio de 2019 (segunda-feira)
Hora: 15:30
Local: B106-a – Bloco B - CT – Instituto de Matemática - UFRJ
Resumo: A well-known conjecture states that a random symmetric n-by-n matrix with entries in {-1,1} is singular with probability 2^{-n+o(1)}. In this talk we will show that the probability of this event is at most 2^{-cn^(1/2)}, improving the best known bound 2^{-cn^(1/4)}, which was obtained recently by Ferber and Jain. The main new ingredient is an inverse Littlewood--Offord theorem in Z_p^n that applies under very mild conditions, whose statement is inspired by the method of hypergraph containers. This is a joint work with Marcelo Campos, Robert Morris and Natasha Morrison.
Palestra: Spanning subgraphs of random graphs
Palestrante: Rob Morris (IMPA)
Data: 29/04/2019 (segunda-feira)
Horário: 15:30h
Local: Sala B106-a (Bloco B - CT), Instituto de Matemática - UFRJ
Resumo: Let H be a graph on n vertices with maximum degree at most d. What is the threshold for the appearance of H in the Erdos-Renyi random graph G(n,p)? A well-known conjecture states that for every such H the threshold is at most n^{-2/(d+1)} (log n)^{O(1)}, and this has been proved for "nowhere dense" graphs by Riordan, and for graphs with bounded components by Johansson, Kahn and Vu. In this talk we will discuss some recent progress on this conjecture for odd values of d.
Palestra: Critical scaling for an anisotropic percolation model on Z2
Palestrante: Maria Eulalia Vares (IM-UFRJ)
Data: 27 de maio de 2019 (segunda-feira)
Hora: 15h40
Local: Sala B106-a (Bloco B - CT), Instituto de Matemática - UFRJ
Resumo: We consider an anisotropic finite-range bond percolation model on Z2 . On each horizontal layer Hi = {(x, i): x ∈ Z} we have edges h(x, i),(y, i)i for 1 ≤ |x − y| ≤ N. There are also vertical edges connecting two nearest neighbor vertices on distinct lines h(x, i),(x, i + 1)i for x, i ∈ Z. On this graph we consider the following anisotropic independent percolation model: horizontal edges are open with probability 1/(2N), while vertical edges are open with probability ∈ to be suitably tuned as N grows to infinity. The main result tells that if ∈ = κN− 2/5, then we see a phase transition in κ: there exist positive and finite constants C1 , C2 so that there is no percolation if κ < C1 while percolation occurs for κ > C2 .
Palestra: Stationary states of symmetric exclusion processes with complex boundary dynamics
Palestrante: Tiecheng Xu (IMPA)
Data: 15 de abril de 2019 (segunda-feira)
Horário: 15:30h
Local: Sala B106-a (Bloco B - CT), Instituto de Matemática - UFRJ
Resumo: In this talk we will discuss the stationary sates of the one-dimensional, boundary driven, symmetric exclusion processes with some non-reversible boundary dynamics. We mainly focus on the exclusion processes whose boundary dynamics are the small perturbation of flipping dynamics. I am going to explain how to derive the hydrostatic limit of this type of processes using duality techniques. If time permits, I will also mention the results for the processes with some other types of boundary dynamics. Joint work with C. Erignoux and C. Landim.
