TY - JOUR
T1 - Reducing exit-times of diffusions with repulsive interactions
AU - Chaudru de Raynal, Paul-Eric
AU - Duong, Manh Hong
AU - Monmarché, Pierre
AU - Tomaševic, Milica
AU - Tugaut, Julian
PY - 2023/7/31
Y1 - 2023/7/31
N2 - In this work we prove a Kramers’ type law for the low-temperature behavior of the exittimes 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.
AB - In this work we prove a Kramers’ type law for the low-temperature behavior of the exittimes 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.
UR - https://doi.org/10.1051/ps/2023012
U2 - 10.1051/ps/2023012
DO - 10.1051/ps/2023012
M3 - Article
VL - 27
SP - 723
EP - 748
JO - ESAIM: Probability and Statistics
JF - ESAIM: Probability and Statistics
ER -