## Seminários de probabilidade – Primeiro Semestre de 2022

As palestras ocorrem no Zoom (link para a sala) **às segundas-feiras às 15h**, a menos de algumas exceções devidamente indicadas.

*Todas as palestras são em inglês.*

**Lista completa (palestras futuras podem sofrer alterações)**

(excepcionalmente às 15h30 e exclusivamente em formato __presencial__ na sala B106B, Centro de Tecnologia)

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This is a joint work with Lucas R. de Lima, A. Hinsen, B. Jahnel and Daniel Valesin.

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Joint work with Luiz Renato Fontes and Susana Frómeta.

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Joint work with Francis Comets and Joseba Dalmau.

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Joint work with Francesca Collet and Elena Magnanini (available at https://arxiv.org/abs/2105.06312).

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__presencial__na sala B106B, Centro de Tecnologia)

This is a joint work with Mikhail Menshikov and Andrew Wade.

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Under the same hypothesis of [{em Ann. Probab. 40 (5), 2012}}] (bounded jumps, uniform ellipticity) and with a sequence ${p_n}_{n ge 1}$ which decays polynomially, namelly $p_n = mathcal{C}n^{-beta} wedge 1$ with $beta > 0$ and $mathcal{C}$ is a positive constant, we show a series of results for the $p_n$-GERW depending on the value of $beta$ and on the dimension. Specifically, for $beta < 1/6$ and $dgeq 2$, we show that the $p_n$-GERW has a positive probability of never returning to the origin in the drift direction, for $beta > 1/2$, $dgeq 2$ and $beta=1/2$ and $d=2$ we obtain, under certain conditions, a Functional Central Limit Theorem. Finally, for $beta=1/2$ and $d ge 4$ we obtain, under suitable conditions, that the $p_n$-Name{} is a tight process, and every limit point $Y$ satisfies $W_t cdot ell + c_1 sqrt{t} preceq Y_t cdot ell preceq W_t cdot ell + c_2 sqrt{t}$ where $c_1$ and $c_2$ are positive constants, $W$ is a Brownian motion and $ell$ is the direction of the drift.

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Joint work with Florian Henning.

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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).

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This is a joint work with Daniel Y. Takahashi (Ice/UFRN).

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Joint work with Nguyen Tong Xuan.