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04 04 NOTICIA IMA Relative entropy and sharp convergence to stationarity 1Título: Relative entropy and sharp convergence to stationarity of the exclusion process

Palestrante : Milton Jara (IMPA)
Data : 11/04/2022
Horário : 15:00h (Rio de Janeiro local time)
Local : Transmissão online

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Resumo: After comprehensive work by Lacoin et al., the convergence to equilibrium of the one-dimensional exclusion process is well understood. In particular, the mixing time and cut-off window are explicitly known. For the particular example of the reversible exclusion process in contact with reservoirs, we show how the mixing time depends on initial conditions which are relevant in the hydrodynamic limit of the exclusion process. The proof relies on log-Sobolev inequalities, relative entropy methods and the CLT for the density of particles. Joint work with Patricia Gonçalves (Lisbon), Rodrigo Marinho (Porto Alegre) and Otávio Menezes (West Lafayette).

All the talks are held in English. 

More complete information about the seminars will be available at HERE.

28 02 IM Noticia ProbabilityWebinarTítulo: Sparse Markov Models for High-dimensional Inference

Palestrante: Daniel Y. Takahashi (Ice/UFRN)
Data: 07/03/2022
Horário: 15:00h
Local: Transmissão online

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Resumo: Finite order Markov models are theoretically well-studied models for dependent categorical data. Despite their generality, application in empirical work when the order is larger than one is quite rare. Practitioners avoid using higher order Markov models because (1) the number of parameters grows exponentially with the order, (2) the interpretation is often difficult. Mixture of transition distribution models (MTD) were introduced to overcome both limitations. MTD represent higher order Markov models as a convex mixture of single step Markov chains, reducing the number of parameters and increasing the interpretability. Nevertheless, in practice, estimation of MTD models with large orders is still limited because of the curse of dimensionality and high algorithm complexity. Here, we prove that if only few lags are relevant we can consistently and efficiently recover the lags and estimate the transition probabilities of high order MTD models. The key innovation is a recursive procedure for the selection of the relevant lags of the model. Our results are based on (1) a new structural result of the MTD and (2) an improved martingale concentration inequality. Our theoretical results are illustrated through simulations.

All the talks are held in English.

More complete information about the seminars will be available at HERE.

01 02 Noticia IM ProbabilitySeminarTítulo: On random processes with variable length

Palestrante: Alex Dias Ramos (UFPE)
Data: 07/02/2022
Horário: 15hrs
Local: Transmissão online

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Resumo: In most of the theoretical research about random systems with local interaction, the supposition that the set of particles, also called the space, does not change during the evolution is widely adopted. This supposition, which we call constant length, is not the only possible one. We will consider another approximation, called variable length. In this talk, for a class of one-dimensional particle processes with discrete-time, where its components are located in the integers set, we shall present a general theory and analyze (in a theoretical and numerical way) some random processes, studied by me with co-authors, which were motivated by this new paradigm.

All the talks are held in English.

More complete information about the seminars will be available at HERE.

Organizers: Giulio Iacobelli and Maria Eulalia Vares

15 02 IM Probability NotíciaTítulo: On random walks that build their own domain

Palestrante: Rodrigo Ribeiro (University of Colorado Boulder)
Data: 21/02/2022
Horário: 15:00h
Local: Transmissão online

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Resumo: In this talk, we will discuss the dichotomy recurrence/transience and ballisticity in the context of a class of random walks that build their own domain. At each step of the walker on its domain, a random number of new vertices is attached to the walker's position. We will present distributional conditions over this random number of new vertices for which we observe distinct sharp behavior on the walker. We also discuss structural results, that is, when this process is seen as a random graph model, the walker is capable of generating trees whose degree distribution approaches a power-law.

All the talks are held in English.

More complete information about the seminars will be available at HERE.

Sincerely,

Organizers: Giulio Iacobelli and Maria Eulalia Vares

19 01 IM Seminar NoticiaTítulo: Probabilistic cellular automata with Bernoulli invariant measures

Palestrante: Siamak Taati (American University of Beirut)
Data: 24/01/2022
Horário: 15hrs
Local: Transmissão online

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Resumo: I will sketch a proof of the following result: If a positive-rate probabilistic cellular automaton has a Bernoulli invariant measure, then it is ergodic, meaning that its distribution starting from any configuration converges (exponentially fast) to that Bernoulli measure. The same result holds for (continuous-time) interacting particle systems. The proof is based on the entropy method, but unlike the usual entropy arguments, does not require the shift-invariance of the starting measure. This result has a practical implication concerning the inevitability of heat dissipation in computers which I will briefly discuss. This is a joint work with Irène Marcovici.

All the talks are held in English.

More complete information about the seminars will be available at HERE.

Those who do not wish to receive our next announcements may simply send an email to <eulalia@im.ufrj.br>; asking to be removed from the list.

Thanks for circulating this information.

Sincerely,

Organizers: Giulio Iacobelli and Maria Eulalia Vares

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