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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>February 8</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><b>Eva </b></span><b><span style="font-family:"Calibri","sans-serif"" lang="EN-US">Löcherbach (</span></b><b><span lang="EN-US">Université Paris<span> </span>I)</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">Conditional propagation of chaos for systems of
interacting neurons with random synaptic weights</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: We study the stochastic system of
interacting neurons introduced in De Masi et al 2015, in a diffusive scaling. The
system consists of N neurons, each spiking randomly with rate depending on its
membrane potential. At its spiking time, the potential of the spiking
neuron is reset to 0 and all other neurons receive an additional amount
of potential which is a centred random variable of order 1 / \sqrt (N).
In between successive spikes, each neuron's potential follows
a deterministic flow. We prove the convergence of the system, as the
number of neurons tends to infinity, to a limit nonlinear jumping stochastic
differential equation driven by Poisson random measure and an additional
Brownian motion W which is created by the central limit theorem. This
Brownian motion is underlying each particle's motion and induces a common noise
factor for all neurons in the limit system. <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">Conditionally on W, the different neurons are
independent in the limit system. This is the ``conditional propagation of
chaos'' property. We prove the well-posedness of the limit equation by adapting
the ideas of Graham 1992 to our frame. To prove the convergence in distribution
of the finite system to the limit system, we introduce a new martingale problem
that is well suited for our framework. The uniqueness of the limit is deduced
from the exchangeability of the underlying system.<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">This is a joint work with Xavier Erny and
Dasha Loukianova, both of university of Evry. <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>
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