Título: On the convergence of the Drainage Network Model with Branching
Palestrante: Rafael Souza dos Santos (IM-UFRJ)
Data: 25/10/2021
Horário: 15:00hrs às 16:00hrs
Local: Transmissão online
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Resumo: We introduce the Drainage Network with Branching, which is a system of coalescing random walks with paths that can branch and that exhibit some dependence before coalescence. It extends the Drainage Network model introduced by Gangopadhyay, Roy and Sarkar in 2004, by allowing the paths to branch. We also study the convergence of the Drainage Network with Branching, under diffusive scaling, to the Brownian Web or Net, according to specific conditions for the branching probability. We show that based on the specification of the branching probability, we can have convergence to the Brownian Web or we can have a tight family such that any weak limit point contains a Brownian Net. In the latter case, we conjecture that the limit is indeed the Brownian Net. This is a joint work with Glauco Valle (IM-UFRJ) and Leonel Zuaznabar (IME-USP).
All the talks are held in English.
The videos of the online seminars are available:
For the second semester, a few days after each meeting the video should be available at HERE.
Título: Structure recovery for partially observed discrete Markov random fields on graphs
Palestrante: Florencia Leonardi (IME-USP)
Data: 18/10/2021
Horário: 15:00hrs às 16:00hrs
Local: Transmissão online
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Resumo: Discrete Markov random fields on graphs, also known as graphical models in the statistical literature, have become popular in recent years due to their flexibility to capture conditional dependency relationships between variables. They have already been applied to many different problems in different fields such as Biology, Social Science, or Neuroscience. Graphical models are, in a sense, finite versions of general random fields or Gibbs distributions, classical models in stochastic processes. This talk will present the problem of estimating the interaction structure (conditional dependencies) between variables by a penalized pseudo-likelihood criterion. First, I will consider this criterion to estimate the interaction neighborhood of a single node, which will later be combined with the other estimated neighborhoods to obtain an estimator of the underlying graph. I will show some recent consistency results for the estimated neighborhood of a node and any finite sub-graph when the number of candidate nodes grows with the sample size. These results do not assume the usual positivity condition for the conditional probabilities of the model as it is usually assumed in the literature of Markov random fields. These results open new possibilities of extending these models to situations with sparsity, where many parameters of the model are null. I will also present some ongoing extensions of these results to processes satisfying mixing type conditions. This talk is based on a joint work with Iara Frondana and Rodrigo Carvalho and some work in progress with Magno Severino.
Todas os seminários são ministrados em inglês.
Os vídeos dos seminários passados estão disponíveis nos links abaixo:
Para o segundo semestre, alguns dias depois dos seminários, às gravações ficaram disponíveis AQUI.
Título: About discrete Bak-Sneppen model
Palestrante: Stanislav Volkov (Lund University)
Data: 29/09/2021
Horário: 13:00h
Local: Transmissão online
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ID da reunião: 958 0581 3232
Resumo: The discrete version of the famous Bak-Sneppen model is a Markov chain on the space of {0,1} sequences of length n with periodic boundary conditions, which runs as follows. Fix some 00.54. This result is indeed correct, however, its proof is not. I shall present the rigorous proof of the Barbay and Kenyon's result, as well as some better bounds for the critical p.
Título: Contact process under heavy-tailed renewals on finite graphs
Palestrante: Luiz Renato Fontes (IME-USP)
Data: 04/10/2021
Horário: 15:00hrs às 16:00hrs
Local: Transmissão online
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Resumo: We look at the contact process with ordinary rate lambda exponential infections and heavy tailed cures, attracted to an alpha-stable law with alpha < 1, on a finite graph of size k. Our aim is to ascertain conditions on alpha and k such that the critical lambda for survival of the infection vanishes. We obtain nearly sharp (in a sense to be clarified) bounds on the critical k, k_c = k_c(alpha), which is always a finite number, such that the infection dies out almost surely for any lambda < infty at and below k_c; and there is positive probability of survival for any lambda > 0 above k_c. This is joint work with Pablo Almeida Gomes and Rémy Sanchis, published recently, in Bernoulli 27(3).
Todas os seminários são ministrados em inglês.
Os vídeos dos seminários passados estão disponíveis nos links abaixo:
Para o segundo semestre, alguns dias depois dos seminários, às gravações ficaram disponíveis AQUI.
Título: First hitting distribution in different regimes: a probabilistic proof of Cooper&Frieze's First Visit Time Lemma
Palestrante: Elisabetta Scoppola (Università Roma Tre)
Data: 27/09/2021
Horário: 15:00hrs às 16:00hrs
Local: Transmissão online
Confira AQUI o link para a transmissão.
Resumo: I present results recently obtained with Francesco Manzo e Matteo Quattropani. We present an alternative proof of the so-called First Visit Time Lemma (FVTL), originally presented by Cooper and Frieze. We work in the original setting, considering a growing sequence of irreducible Markov chains on n states. We assume that the chain is rapidly mixing and with a stationary measure with no entry being either too small nor too large. Under these assumptions, the FVTL shows the exponential decay of the distribution of the hitting time of a given state x, for the chain started at stationarity, up to a small multiplicative correction. While the proof by Cooper and Frieze is based on tools from complex analysis, and it requires an additional assumption on a generating function, we present a completely probabilistic proof, relying on the theory of quasi-stationary distributions and on strong-stationary times arguments. In addition, under the same set of assumptions, we provide some quantitative control on the Doob's transform of the chain on the complement of the state x. I will also discuss the relation of this result with general results, previously obtained, providing an exact formula for the first hitting distribution via conditional strong quasi-stationary times.
Todas os seminários são ministrados em inglês.
Os vídeos dos seminários passados estão disponíveis nos links abaixo:
Para o segundo semestre, alguns dias depois dos seminários, às gravações ficaram disponíveis AQUI.
