[ABE-L] Próximo seminário (online) de probabilidade - 7 de junho

[Maria Eulalia Vares]

*Probability Webinar -   IM-UFRJ *



Dear colleagues,

Our next online seminar will be held on Monday, *June 7, * from *3 p.m. to
4 p.m*. (Rio de Janeiro local time)

The GoogleMeet link for the seminar is  https://meet.google.com/uew-ehhn-kby


Speaker:   *Hubert Lacoin (IMPA)*

Title: *Fast mixing time for the exclusion process in a random environment*

Abstract:  We consider a system of $k$ particles on a segment of size $N$.
Its rules of evolution are the following: a particle at site $x \in \{1
,\dots, N\}$ jumps to $x+1$  with rate $\omega_x$ and to $x-1$ with rate
$1-\omega_x$ where $\omega_x\in (0,1)$, and a jump is cancelled if the site
is already occupied. We consider the case where $(\omega_x)^N_{x=1}$ is
(the fixed realization of) a sequence of IID random variables. Assuming
that $\mathbb E[ \log\frac{1-\omega_x}{\omega_x}]\ne 0$ (that is,
transience of the random environment), we prove that this particle systems
mixes fast, in the sense that the time that it requires for its
distribution to get close to the equilibrium state grows like a power of
$N$. We present a lower bound for the power in mixing time which we
conjecture to be sharp.

Joint work with S. Yang, IMPA.



All the talks are held in English.

The videos of the online seminars held in 2020 are available at
http://www.dme.ufrj.br/?page_id=2885

For the 2021 series, a few days after each meeting the video should be
available at http://www.dme.ufrj.br/?page_id=3027



Thanks for circulating this information.

Sincerely,
Organizers: Guilherme Ost and Maria Eulalia Vares
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