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<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><b><span style="font-size:12pt;line-height:115%" lang="EN-US">Probability Webinar -<span>   </span>IM-UFRJ <span></span></span></b></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US"><span> </span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Dear colleagues,<span> 
</span><span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Our next online seminar will be held on Monday, <b>June 7, </b><span> </span>from <b>3 p.m. to 4 p.m</b>. (Rio de Janeiro
local time)<span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">The GoogleMeet link for the seminar is  </span><a href="https://meet.google.com/uew-ehhn-kby" style="color:blue;text-decoration:underline" target="_blank"><span style="font-size:12pt;line-height:115%" lang="EN-US">https://meet.google.com/uew-ehhn-kby</span></a><span style="font-size:12pt;line-height:115%" lang="EN-US"> 
<span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%">Speaker:<span>   </span><b>Hubert Lacoin (IMPA)<span></span></b></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Title:
</span><b><span style="font-size:12pt;line-height:115%" lang="EN-US">Fast mixing
time for the exclusion process in a random environment<span></span></span></b></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Abstract:
<span> </span></span><span lang="EN-US">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. <span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span lang="EN-US">Joint work
with S. Yang, IMPA. <span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span lang="EN-US"><span> </span></span></p>

<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">All the talks
are held in English. <span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">The videos of the online seminars held in 2020 are
available at <a href="http://www.dme.ufrj.br/?page_id=2885" target="_blank">http://www.dme.ufrj.br/?page_id=2885</a><span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">For the 2021 series, a few days after each meeting the
video should be available at <a href="http://www.dme.ufrj.br/?page_id=3027" target="_blank">http://www.dme.ufrj.br/?page_id=3027</a><span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US"><span> </span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Thanks for circulating this information. <span></span></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%" lang="EN-US">Sincerely, <br>
Organizers: Guilherme Ost and Maria Eulalia Vares<span></span></span></p>





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