Limit Properties of Langevin Models and

Il y a 2 mois

Lyon, France Université Jean Monnet Saint Etienne Temps plein

Réf
- **ABG-112389**
- Sujet de Thèse- 22/03/2023- Contrat doctoral- Université Jean Monnet Saint Etienne- Lieu de travail- Saint-Etienne - Auvergne-Rhône-Alpes - France- Intitulé du sujet-
- Champs scientifiques- Mathématiques
- Mots clés- Kinetic models, Metastability and related large deviation principles, Cooperative multi-agent systems**Description du sujet**:
The aim of this thesis is to investigate the asymptotic behaviour, at different characteristic scales (long-time, zero
noise and large population), and the metastability properties of a class of stochastic kinetic models depicting cooperative multi-agent systems.

While agglomerating systems have been well-studied in over-damped or in zero-noise regimes, little is effectively known for the noisy Cucker-Smale model notably an agglomerating-alignment setting. The principal focus of the thesis will be so to study this limit behaviour with a metastability viewpoint, and estimating how the first time that alignment and a (fixed) agglomeration are destroyed or restored in the small-noise limit, in the situations of a finite or an asymptotically large population. In this context, stochastically perturbed Cucker-Smale models with uniformly convex and multistable exogenous potential (modelling distinct attracting sources or asymptotic leading directions) will be first considered.

**Prise de fonction**:

- 01/09/2023**Nature du financement**:

- Contrat doctoral**Précisions sur le financement**:
**Présentation établissement et labo d'accueil**:

- Université Jean Monnet Saint EtienneThe PhD thesis will be hosted at the Université Jean Monnet (UJM). The UJM is a multi-disciplinary university

**Intitulé du doctorat**:

- Doctorat de Mathématiques Appliquées**Pays d'obtention du doctorat**:

- France**Etablissement délivrant le doctorat**:

- UNIVERSITE JEAN MONNET SAINT-ETIENNE**Ecole doctorale**:

- Sciences, ingénierie, santéThis thesis is addressed to students with a strong background on probability theory, stochastic modelling and stochastic analysis. Skills in dynamical systems, limit theorems for stochastic processes and large deviations techniques will be appreciated.- 17/04/2023

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