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Article Dans Une Revue ESAIM: Probability and Statistics Année : 2023

Reducing exit-times of diffusions with repulsive interactions

Résumé

In this work we prove a Kramers' type law for the low-temperature behavior of the exit-times from a metastable state for a class of self-interacting nonlinear diffusion processes. Contrary to previous works, the interaction is not assumed to be convex, which means that this result covers cases where the exit-time for the interacting process is smaller than the exit-time for the associated non-interacting process. The technique of the proof is based on the fact that, under an appropriate contraction condition, the interacting process is conveniently coupled with a non-interacting (linear) Markov process where the interacting law is replaced by a constant Dirac mass at the fixed point of the deterministic zero-temperature process.

Dates et versions

hal-03762603 , version 1 (28-08-2022)

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Paul-Eric Chaudru de Raynal, Manh Hong Duong, Pierre Monmarché, Milica Tomasevic, Julian Tugaut. Reducing exit-times of diffusions with repulsive interactions. ESAIM: Probability and Statistics, 2023, 27, pp.723-748. ⟨10.1051/ps/2023012⟩. ⟨hal-03762603⟩
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