Exit-time of mean-field particles system
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 399-407

The current article is devoted to the study of a mean-field system of particles. The question that we are interested in is the behaviour of the exit-time of the first particle (and the one of any particle) from a domain $$ on ℝ$$ as the diffusion coefficient goes to 0. We establish a Kramers’ type law. In other words, we show that the exit-time is exponentially equivalent to $$, H$$ being the exit-cost. We also show that this exit-cost converges to some quantity H.

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DOI : 10.1051/ps/2019028
Classification : 60F10, 60J60, 60H10
Keywords: Exit-problem, large deviations, interacting particle systems, mean-field systems 
@article{PS_2020__24_1_399_0,
     author = {Tugaut, Julian},
     title = {Exit-time of mean-field particles system},
     journal = {ESAIM: Probability and Statistics},
     pages = {399--407},
     year = {2020},
     publisher = {EDP Sciences},
     volume = {24},
     doi = {10.1051/ps/2019028},
     mrnumber = {4153635},
     zbl = {1455.60047},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps/2019028/}
}
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Tugaut, Julian. Exit-time of mean-field particles system. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 399-407. doi: 10.1051/ps/2019028

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