<div dir="ltr"><div class="gmail_quote"><div dir="ltr" class="gmail_attr"><br></div><div dir="ltr"><div><br></div><div><p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><b><span lang="EN-US" style="font-size:12pt;line-height:115%">Probability Webinar - IM-UFRJ </span></b></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><b><span lang="EN-US" style="font-size:12pt;line-height:115%"> </span></b></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Dear colleagues,
</span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Our next
online seminar will be held on Monday, <b>September
27, </b> from <b>3 p.m. to 4 p.m</b>.
(Rio de Janeiro local time)</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" style="font-size:12pt;line-height:115%">The Zoom link for the seminar is </span><span lang="EN-US"></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><a href="https://us02web.zoom.us/j/83698166702?pwd=ejFxYmh3dVk5b3J3SG0wMWxEVnVrUT09" style="color:blue" target="_blank"><span lang="EN-US" style="font-family:Arial,sans-serif;color:rgb(17,85,204);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">https://us02web.zoom.us/j/83698166702?pwd=ejFxYmh3dVk5b3J3SG0wMWxEVnVrUT09</span></a><span lang="EN-US"></span></p><p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><br></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span style="font-size:12pt;line-height:115%">Speaker: </span><span><b>Elisabetta Scoppola (Università
Roma Tre)</b></span><b><span style="font-size:12pt;line-height:115%"></span></b></p>
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<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">Title:
</span><b><span lang="EN-US">First hitting distribution in different regimes:</span></b><b><span lang="EN-US" style="font-size:12pt;line-height:115%"> a probabilistic proof of
Cooper&Frieze's First Visit Time Lemma</span></b><span lang="EN-US"></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" style="font-size:12pt;line-height:115%">Abstract:
</span><span lang="EN-US" style="font-size:12pt;line-height:115%"> </span><span lang="EN-US">I present results recently obtained with
Francesco Manzo e Matteo Quattropani. </span><span lang="EN-US" style="font-size:12pt;line-height:115%">We present an alternative
proof of the so-called First Visit Time Lemma (FVTL), originally presented by
Cooper and Frieze. We work in the original setting, considering a growing
sequence of irreducible Markov chains on n states. We assume that the chain is
rapidly mixing and with a stationary measure with no entry being either too
small nor too large. Under these assumptions, the FVTL shows the exponential
decay of the distribution of the hitting time of a given state x, for the chain
started at stationarity, up to a small multiplicative correction. While the
proof by Cooper and Frieze is based on tools from complex analysis, and it
requires an additional assumption on a generating function, we present a
completely probabilistic proof, relying on the theory of quasi-stationary
distributions and on strong-stationary times arguments. In addition, under the
same set of assumptions, we provide some quantitative control on the Doob's
transform of the chain on the complement of the state x.</span><span lang="EN-US"></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" style="font-size:12pt;line-height:115%">I will also discuss the relation of this result with
general results, previously obtained, providing an exact formula for the first
hitting distribution via conditional strong quasi-stationary times.</span><span lang="EN-US"></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" style="font-size:12pt;line-height:115%"> </span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">All the talks
are held in English. </span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">The videos of
the online seminars are available:</span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt;line-height:115%">2020 - <a href="http://www.dme.ufrj.br/?page_id=2885" target="_blank">http://www.dme.ufrj.br/?page_id=2885</a></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" style="font-size:12pt;line-height:115%">2021-1 -
<a href="http://www.dme.ufrj.br/?page_id=3027" target="_blank">http://www.dme.ufrj.br/?page_id=3027</a></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" style="font-size:12pt;line-height:115%">For the second semester, a few days after each meeting
the video should be available at <a href="http://www.dme.ufrj.br/?page_id=3178" target="_blank">http://www.dme.ufrj.br/?page_id=3178</a></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" style="font-size:12pt;line-height:115%">Thanks for circulating this information. </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" style="font-size:12pt;line-height:115%">Sincerely, <br>
Organizers: Guilherme Ost and Maria Eulalia Vares</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" style="font-size:12pt;line-height:115%"> </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" style="font-size:12pt;line-height:115%"> </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" style="font-size:12pt;line-height:115%"> </span></p>
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