00:00:00 / 00:00:00

Propagation of Chaos and Poisson Hypothesis for Replica Mean-Field Models

De Michel Davydov

Apparaît dans la collection : 2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

In order to model neural computations resulting from myriads of neuronal interactions, intensity-based spiking neural networks are commonly used. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas of the networks of interest. In contrast with classical thermodynamic mean-fields, interaction couplings do not scale with the number of neurons and preserve both the geometry of the network and the finite-size correlations. In the limit of an infinite number of replicas, these networks become analytically tractable under the so-called Poisson Hypothesis, which postulates that replicas become asymptotically independent and arrivals to a given neuron become Poisson distributed. This hypothesis is often conjectured or numerically validated but not proven. We show the validity of the Poisson Hypothesis for large classes of processes that include for example Galves-Löcherbach models.

Informations sur la vidéo

Données de citation

  • DOI 10.57987/IHP.2022.T1.WS2.020
  • Citer cette vidéo Davydov, Michel (03/02/2022). Propagation of Chaos and Poisson Hypothesis for Replica Mean-Field Models. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.020
  • URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.020

Dernières questions liées sur MathOverflow

Pour poser une question, votre compte Carmin.tv doit être connecté à mathoverflow

Poser une question sur MathOverflow




Inscrivez-vous

  • Mettez des vidéos en favori
  • Ajoutez des vidéos à regarder plus tard &
    conservez votre historique de consultation
  • Commentez avec la communauté
    scientifique
  • Recevez des notifications de mise à jour
    de vos sujets favoris
Donner son avis