<div dir="ltr"><div class="gmail_quote gmail_quote_container"><br><br><div dir="ltr"><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 1</b>,<b> </b>from <b>3:30
p.m. to 4:30 p.m</b>. (Rio de Janeiro local time). </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">It will be held through
Google Meet</span><b><span lang="EN-US" style="font-size:12pt"> </span></b><a href="https://meet.google.com/idy-jhss-htx" style="color:rgb(5,99,193)" target="_blank"><b><span style="font-size:12pt">https://meet.google.com/idy-jhss-htx</span></b></a><span lang="EN-US" style="font-size:12pt"></span></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 lang="EN-US" style="font-size:12pt;line-height:115%;color:black">Speaker: <b>  Minmin Wang (University of Sussex)</b></span></p>

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<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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Title: <b>Exchangeability
in Continuum Random Trees</b></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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Abstract: De Finetti’s
Theorem states that all N-indexed exchangeable sequences of real-valued random
variables are mixings of i.i.d sequences. For real-valued random processes with
exchangeable increments on [0, 1], Kallenberg’s 1973 result provides a complete
characterisation of these processes via another mixing relationship.</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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Continuum random trees
are random tree-like metric spaces that arise naturally as scaling limits of
various models of discrete random trees. In this talk, we will focus in
particular on two subclasses of continuum random trees: the so-called stable
trees and inhomogeneous continuum random trees. An analogue of Kallenberg’s
Theorem for continuum random trees first appeared as a claim in a 2004 paper by
Aldous, Miermont and Pitman. They suggested that, in much the same way that a
stable bridge process on [0, 1] is a mixing of certain extremal exchangeable
processes, stable trees are mixings of inhomogeneous continuum random trees.</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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">We present an outline
of a rigorous argument supporting this claim, based on a novel construction
that applies to both classes of trees. We will also briefly discuss some
implications of this result on critical random graphs.</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;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">The talk is based on
the paper <i>Stables trees as mixings of inhomogeneous continuum random trees,</i>
Stochastic Processes and their Applications 175, 2024, 104404.</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></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>
</div><div><br></div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><br></div></div></div></div>