Electronic Communications in Probability

A simple proof of a Kramers’ type law for self-stabilizing diffusions

Julian Tugaut

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We provide a new proof of a Kramers’ type law for self-stabilizing diffusion. These diffusions correspond to the hydrodynamical limit of a mean-field system of particles and may be seen as the probabilistic interpretation of the granular media equation. We use the same hypotheses as the ones used in the work “Large deviations and a Kramers’ type law for self-stabilizing diffusions” by Herrmann, Imkeller and Peithmann in which the authors obtain a first proof of the statement.

Article information

Electron. Commun. Probab., Volume 21 (2016), paper no. 11, 7 pp.

Received: 5 March 2015
Accepted: 8 February 2016
First available in Project Euclid: 15 February 2016

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Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 60J60: Diffusion processes [See also 58J65] 60H10: Stochastic ordinary differential equations [See also 34F05]

self-stabilizing diffusion exit time large deviations coupling method

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Tugaut, Julian. A simple proof of a Kramers’ type law for self-stabilizing diffusions. Electron. Commun. Probab. 21 (2016), paper no. 11, 7 pp. doi:10.1214/16-ECP4160. https://projecteuclid.org/euclid.ecp/1455560035

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