<div dir="ltr"><div class="gmail_quote gmail_quote_container"><div dir="ltr"><div><br clear="all"></div><div><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="margin:0cm;text-align:justify;line-height:normal;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt"> </span></p>

<p class="MsoNormal" style="margin:0cm;text-align:justify;line-height:normal;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt">Our next seminar will be
held on Monday, <b>September 29</b>,<b> </b>from <b>3:30
p.m. to 4:30 p.m</b>. (Rio de Janeiro local time).  The meeting will take place at room </span><b><span lang="EN-US" style="font-size:12pt">C116-
Bloco C - CT</span></b><b><span lang="DE" style="font-size:12pt"> – Instituto de Matemática – UFRJ. </span></b><span lang="DE" style="font-size:12pt">There will be no transmission
online. </span><b><span lang="EN-US" style="font-size:12pt"></span></b></p>

<p class="MsoNormal" style="line-height:12.65pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;margin:0cm 0cm 10pt;font-size:11pt;font-family:Calibri,sans-serif"><span lang="DE" style="font-size:12pt"> </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%;color:black">Speaker: <b>  </b></span>Ioannis
Tsokanos (UNESP, São José do Rio Preto)</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%;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Title: </span><b><span style="font-size:12pt;line-height:115%">Randomisation in the Josephus Problem</span></b><b><span lang="EN-US" style="font-size:12pt;line-height:115%;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"></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%;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Abstract: </span>The Josephus problem is a well--studied elimination problem consisting in
determining the position of the survivor after repeated applications of a
deterministic rule removing one person at a time from a given group.</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%">In this
talk, we introduce a natural probabilistic variant of this process. More
precisely, in this variant, the survivor is determined after performing a
succession of Bernouilli trials with parameter <i>p</i> designating each time
the person to remove. When the number of participants tends to infinity, the
main result characterises the limit distribution of the position of the
survivor with an increasing degree of precision as the parameter approaches the
unbiased case <i>p=1/2</i>. Then, the convergence rate to the position of the
survivor is obtained in the form of a Central-Limit Theorem.</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%">A number of
other variants of the suggested probabilistic elimination process are also
considered. They each admit a specific limit behavior which, in most cases, is
stated in the form of an open problem.</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%;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"> </span></p>

<p class="MsoNormal" style="line-height:normal;margin:0cm 0cm 10pt;font-size:11pt;font-family:Calibri,sans-serif"><span lang="EN-US" style="font-size:12pt">More complete information
about the seminars can be found at</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"><a href="https://ppge.im.ufrj.br/seminarios-de-probabilidade/" target="_blank">https://ppge.im.ufrj.br/seminarios-de-probabilidade/</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%">Sincerely, </span><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%">Organizers: Giulio Iacobelli 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></div><span class="gmail_signature_prefix">-- </span><br><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr">Maria Eulalia Vares<div>Professora Titular - Instituto de Matemática - UFRJ</div><div>Coordenadora do Programa de Pós-Graduação em Estatística</div><div><a href="https://ppge.im.ufrj.br/" target="_blank">https://ppge.im.ufrj.br/</a></div><div><br></div></div></div></div>
</div><div><br clear="all"></div><div><br></div><span class="gmail_signature_prefix">-- </span><br><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr">Maria Eulalia Vares<div>Professora Titular - Instituto de Matemática - UFRJ</div><div>Coordenadora do Programa de Pós-Graduação em Estatística</div><div><a href="https://ppge.im.ufrj.br/" target="_blank">https://ppge.im.ufrj.br/</a></div><div><br></div></div></div></div>