Dear colleagues,

this is a gentle reminder of today One World Probability Seminar, details below. The seminar will be held at 15:00 (italian time).

This will be the last seminar of the spring term, we hope to see many of you online!

Luisa and Roger

________________________________ Da: owps-request@lists.bath.ac.uk owps-request@lists.bath.ac.uk per conto di One World Probability ow.probability@gmail.com Inviato: martedì 17 giugno 2025 21:13 A: owps@lists.bath.ac.uk owps@lists.bath.ac.uk Oggetto: [owps] Fwd: next OWPS: Eva Löcherbach and Elisa Marini

The final OWPS of Spring will be on Wednesday, June 18, from 13:00 to 15:00 UTC time.

Title, abstract and the zoom link are below the signature and can be found on the website https://www.owprobability.org/one-world-probability-seminarhttps://protect-eu.mimecast.com/s/-zGkCWqjZFlpkVlsnEyR_?domain=eur01.safelinks.protection.outlook.com.

-----------------------

Probabilistic models for systems of interacting spiking neurons and some words about their mean field limits

E. Löcherbach (Paris 1 Panthéon-Sorbonne University)

I will give an overview of recent results about mean field limits for systems of interacting point processes modeling spiking (biological) neurons. I will start with a short introduction to the functioning of neurons and the modeling of their spiking activity by stochastic integrate and fire models and then focus on a particular class of models which are stochastic intensity based processes. Then we will discuss mean field limits and propagation of chaos results for large homogeneous systems of neurons and see how the limit is described by a McKean-Vlasov type equation driven by Poisson random measure. A second part of the talk is devoted to the study of systems with random synaptic weights in a diffusive scaling. We will see how this setting leads to conditional propagation of chaos and how the convergence can be obtained by means of a new martingale problem. Finally, if time permits, I will also discuss the longtime behavior both of the finite and the limit system of neurons.

The second part of the talk is based on joint work with Xavier Erny and Dasha Loukianova.

Strong conditional propagation of chaos for systems of interacting particles with nearly stable jumps

E. Marini (Dauphine-PSL Paris)

We consider a system of N interacting particles, described by SDEs driven by Poisson random measures, where the coefficients depend on the empirical measure of the system. Every particle jumps with a rate depending on its position. When this happens, all the other particles of the system receive the same random kick, distributed according to a heavy-tailed random variable belonging to the domain of attraction of an α-stable law, and scaled by N−1/α, where α ∈ (0, 2) \ {1}. We call these jumps collateral jumps. Moreover, in the case 0 < α < 1, the jumping particle itself undergoes a macroscopic, main jump. Similar systems are used to model networks of interacting neurons; in that context, main and collateral jumps represent, respectively, the hyperpolarization of a neuron after a spike and the synaptic inputs received by post-synaptic neurons from pre-synaptic ones.

We prove that our system satisfies the conditional propagation of chaos property: as N → +∞, the finite particle system converges to an infinite exchangeable system that obeys a McKean–Vlasov SDE driven by an α-stable process. In the limit, the particles become independent, conditionally on the driving α-stable process.

https://polimi-it.zoom.us/j/92945513591?pwd=zjtRwpHoO9kRyQuPPj4o186jXrvg1v.1

Meeting ID: 92945513591

Passcode: 131676