[ABE-L] Próximo seminário (online) de probabilidade - IM-UFRJ - 8 de fevereiro

[Maria Eulalia Vares]

*Probability Webinar -   IM-UFRJ *



Dear colleagues,

Our next online seminar will be held on Monday, *February 8*, from *3 p.m.
to 4 p.m*. (Rio de Janeiro local time)

The GoogleMeet link for the seminar is  https://meet.google.com/uew-ehhn-kby




Speaker:    *Eva **Löcherbach (**Université Paris  I)*

Title: *Conditional propagation of chaos for systems of interacting neurons
with random synaptic weights*

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.

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.

This is a joint work with Xavier Erny and Dasha Loukianova, both of
university of Evry.



All the talks are held in English.

The videos of the online seminars held in 2020 are available at
http://www.dme.ufrj.br/?page_id=2885

For the 2021 series, a few days after each meeting the video should be
available at http://www.dme.ufrj.br/?page_id=3027



Thanks for circulating this information.

Sincerely,
Organizers: Guilherme Ost and Maria Eulalia Vares
-------------- Próxima Parte ----------
Um anexo em HTML foi limpo...
URL: <http://lists.ime.usp.br/pipermail/abe/attachments/20210203/388a61fd/attachment.htm>