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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>March 1st</b>, 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><span lang="EN-US"> </span><a href="https://meet.google.com/uew-ehhn-kby" style="color:blue;text-decoration:underline" target="_blank"><span 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%" 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">Speaker: <span> </span></span><b><span style="font-size:12pt;line-height:115%">Ines Armendariz (UBA) </span></b><span style="font-size:12pt;line-height:115%" lang="EN-US"><span></span></span></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 style="font-size:12pt;line-height:115%" lang="EN-US">Title:
</span><b><span lang="EN-US">Gaussian random permutations and the boson
point process </span></b><b><span style="font-size:12pt;line-height:115%" lang="EN-US"><span></span></span></b></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">Abstract: </span><span lang="EN-US">We construct an infinite
volume spatial random permutation associated to a Gaussian Hamiltonian, which
is parametrized by the point density and the temperature. Spatial random
permutations are naturally related to boson systems through a representation originally
due to Feynman (1953). Bose-Einstein condensation occurs for dimensions 3 or
larger, above a critical density, and is manifest in this representation by the
presence of cycles of macroscopic length. For subcritical densities we define
the spatial random permutation as a Poisson process of finite unrooted loops of
a random walk with Gaussian increments that we call Gaussian loop soup,
analogous to the Brownian loop soup of Lawler and Werner (2004). We also
construct Gaussian random interlacements, a Poisson process of doubly-infinite
trajectories of random walks with Gaussian increments analogous to the Brownian
random interlacements of Sznitman (2010). For dimensions greater than or equal
to 3 and supercritical densities, we define the spatial permutation as the
superposition of independent realizations of the Gaussian loop soup at critical
density and Gaussian random interlacements at the remaining density. We show
some properties of these spatial permutations, in particular that the point
marginal is the boson point process, for any point density.<span></span></span></p>
<p class="MsoNormal" style="line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span lang="EN-US">This is joint work with
P.A. Ferrari and S. Yuhjtman.<span></span></span></p>
<p class="MsoNormal" style="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>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:14pt;line-height:115%" lang="EN-US"><span> </span></span></p>
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