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06 01 IM NoticiaTítulo: Brownian modules of continuité and diffusion approximation

Palestrante: Julien Chevallier (LJK, Université Grenoble Alpes)
Data: 11/01/2021
Horário: 15:00h - 16:00h (Rio de Janeiro local time)
Local: Transmissão Online

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Resumo: Garsia–Rodemich–Rumsey (1971) proved an inequality which has been used to upper-bound the Brownian modules of continuity. In turn, this upper-bound was used by T.G. Kurtz (1976) to prove a strong diffusion approximation result for pure jump processes. However, this proof makes the crucial assumption that jump rates are uniformly bounded. The main objective of this talk is to show how to get rid of this assumption starting back from GRR inequality. The second objective is to show that this scheme of proof is robust to time scaling.

All the talks are held in English.
We take the opportunity to inform that the videos of the online seminars held during 2020 are available HERE.

Regarding this year, a few days after each meeting the video should be available HERE.

21 12 IM Noticia2Título: Renewal Contact Process: phase transition and survival

Palestrante: Daniel Ungaretti (IME-USP)
Data: 04/01/2021
Horario: 15:00 - 16:00 (Horário do Rio de Janeiro)
Local: Transmissão Online

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Resumo: The Contact Process was introduced by Harris in 1974 and models the spread of an infection on a graph. The state of each vertex is either infected or healthy, and there are two competing factors that govern the evolution of the process over time: infected vertices become healthy at rate 1 and healthy vertices can get infected at a rate proportional to its current number of infected neighbors. In two recent papers, Fontes, Marchetti, Mountford and Vares introduced a generalization of the model in which cures are given by renewal processes with some fixed interarrival distribution. I will discuss how the choice of interarrival distribution affects the spread of the infection, focusing on recent developments in which we improved the characterization of the interarrival distributions for which there is phase transition. Joint work with Luiz Renato Fontes, Tom Mountford and Maria Eulália Vares.

30 11 im noticia probabilitywebinarTítulo: Percolation on a randomly stretched lattice

Palestrante: Marcelo Richard Hilário (Dep. de Matemática - UFMG)
Data: 07/12/2020
Horário: 15:00
Local: Transmissão Online

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Resumo: We consider a stretched version of the square lattice where the distances between neighboring vertical columns are given by interarrival intervals of a renewal process. Hence, horizontal edges that link vertices in the same pair of vertical columns have a common random length while every vertical edge has length one. Conditioned on the realization of the lattice, we define a bond percolation model where edges are open with probabilities that depend on their length. We relate the question of whether the model undergoes a non-trivial phase transition to the moments of interarrival times of the renewal process governing the distance among columns. We will also discuss some other related percolation models defined on media with similar types of columnar disorder. Based on a joint work with Marcos Sá, Augusto Teixeira and Remy Sanchis.

All the talks are held in English.

Organizadores: Guilherme Ost and Maria Eulalia Vares

10 12 im noticia probabilitywebinarTítulo: Random walk based algorithms for generating uniform spanning trees

Palestrante: Giulio Iacobelli (IM-UFRJ)
Organizadores: Guilherme Ost e Maria Eulalia Vares
Data: 14/12/2020
Horario: 15:00.a 16:00 (Rio de Janeiro local time)
Local: Transmissão online

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Resumo: The task of efficiently generating uniform spanning trees of a graph has received much attention. A breakthrough came with Aldous-Broder and Wilson's algorithms, which can efficiently generate spanning trees based on random walks. In this work, we study the transient behavior of both algorithms. We introduce the notion of branches, which are paths generated by the two algorithms on particular stopping times. This interpretation is used to show a transient equivalence between the two algorithms on complete graphs. This equivalence yields a hybrid approach to generate uniform spanning trees of complete graphs faster than either of the two algorithms. We also propose a two-stage framework to explore this hybrid approach beyond complete graphs, showing its feasibility in some examples.

All the talks are held in English.

26 11 im noticia probabilitywebinarTítulo: Importance sampling with adaptive winsorization

Palestrante: Paulo Orenstein (IMPA)

Data: 30/11/2020
Local: Transmissão online

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Resumo: Importance sampling is a widely used technique to estimate the properties of a distribution. The resulting estimator is always unbiased, but may sometimes incur huge or infinite variance. This work investigates trading-off some bias for variance by winsorizing the importance sampling estimator using an adaptive thresholding procedure based on the Balancing Principle (also known as Lepskii's Method). This provides a principled way to perform winsorization, with finite-sample optimality guarantees and good empirical performance.