Open Access
2015 Chaoticity of the stationary distribution of rank-based interacting diffusions
Julien Reygner
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Electron. Commun. Probab. 20: 1-20 (2015). DOI: 10.1214/ECP.v20-4063


We consider Brownian diffusions on the real line, interacting through rank-dependent drifts. It is known that in the mean-field limit, such particle systems behave like independent copies of a so-called nonlinear diffusion process. We prove a similar asymptotic behaviour at the level of stationary distributions. Our proof is based on explicit expressions for the Laplace transforms of the stationary distributions of both the particle system and the nonlinear diffusion process, and yields convergence of the marginal distributions in Wasserstein distances of all orders. We highlight the consequences of this result on the study of rank-based models of equity markets, such as the Atlas model.


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Julien Reygner. "Chaoticity of the stationary distribution of rank-based interacting diffusions." Electron. Commun. Probab. 20 1 - 20, 2015.


Accepted: 27 August 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1333.60209
MathSciNet: MR3399811
Digital Object Identifier: 10.1214/ECP.v20-4063

Primary: 60H10
Secondary: 60F05

Keywords: chaoticity , Nonlinear diffusion process , rank-based interacting diffusions , stationary distribution , Wasserstein distance

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