Segue abaixo a programação para o mês de abril do seminário de probabilidade no IM-UFRJ.

Data: 03 de abril de 2017 (segunda-feira)
Hora: 15:30 h
Local: Sala B106a – Bloco B do CT – Instituto de Matemática – UFRJ

Palestrante: Freddy Hernandez (IME-UFF)

Título: Flutuações no equilíbrio para uma modelo discreto do tipo Atlas

Resumo: Consideramos uma versão discreta do chamado “Atlas model”, que corresponde a uma sequência de processos de alcance zero (zero-range) numa linha semi-infinita, com uma fonte na origem e uma densidade de partículas divergente. Mostramos que as flutuações no equilíbrio do modelo são regidas por uma equação do calor estocástica com condições de contorno de Neumann.
Como consequência, mostramos que a corrente de partículas na origem converge para um movimento Browniano fracionário com exponente de Hurst $H = \frac{1}{4}$.

Data: 10 de abril de 2017 (segunda-feira)
Hora: 15:30 h
Local: Sala B106a – Bloco B do CT – Instituto de Matemática – UFRJ

Palestrante: Giulio Iacobelli (PESC/COPPE- UFRJ)

Título: Growing Networks with Random Walks

Resumo: Network growth and evolution is a fundamental theme that has puzzled scientists for the past decades. A number of models have been proposed to capture important properties of real networks, the most famous being the model of Barabási-Albert (BA) which embodies the principle of preferential attachment. A recognized drawback of most proposed network growth models is
the assumption of global information about the network. For example, the BA model requires the knowledge of the degree of every node in the network to randomly choose where a new node will be connected.

In this work we propose and study a network growth model that is purely local. The model is based on a continuously moving random walk that after s steps connects a new node to its current location. Through extensive simulations and theoretical arguments, we analyze the behavior of the model finding a fundamental dependency on the parity of s, where networks with either exponential or heavy-tailed degree distribution can emerge. As s increases, parity dependency diminishes and the model recovers the degree distribution of BA preferential attachment model. The proposed purely local model indicates that networks can grow to exhibit interesting properties even in the absence of any global information.

Joint work with Bernardo Amorim, Daniel Figueiredo, and Giovanni Neglia.

Data: 17 de abril de 2017 (segunda-feira)
Hora: 15:30 h
Local: Sala B106a – Bloco B do CT – Instituto de Matemática – UFRJ

Palestrante: Bernardo Nunes Borges de Lima (Matemática – UFMG)

Título: Truncated long-range percolation on oriented graphs

Resumo:

We consider different problems within the general theme of long-range percolation on oriented graphs. Our aim is to settle the so-called truncation question, described as follows. We are given probabilities that certain long-range oriented bonds are open; assuming that the sum of these probabilities is infinite, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. We give some conditions in which the answer is affirmative. We also translate some of our results on oriented percolation to the context of a long-range contact process. Joint work with Aernout van Enter and Daniel Valesin.

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