5 papers
Long time behavior of killed Feynman-Kac semigroups with singular Schr{ö}dinger potentials
Arnaud Guillin, D I Lu, Boris Nectoux +1
In this work, we investigate the compactness and the long time behavior of killed Feynman-Kac semigroups of various processes arising from statistical physics with very general sin…
Uniform-in-time concentration in two-layer neural networks via transportation inequalities
Arnaud Guillin, Boris Nectoux, Paul Stos
We quantify, uniformly over time and with high probability, the discrepancy between the predictions of a two-layer neural network trained by stochastic gradient descent (SGD) and t…
Quasi-stationarity of the Dyson Brownian motion with collisions
Arnaud Guillin, Boris Nectoux, Liming Wu
In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of…
Generalized Langevin And Nos{é}-hoover Processes Absorbed At The Boundary Of A Metastable Domain
Arnaud Guillin, D I Lu, Boris Nectoux +1
In this paper, we prove in a very weak regularity setting existence and uniqueness of quasi-stationary distributions as well as exponential conver- gence towards the quasi-stationa…
Large deviations of the empirical measures of a strong-Feller Markov process inside a subset and quasi-ergodic distribution
Arnaud Guillin, Boris Nectoux, Liming Wu
In this work, we establish, for a strong Feller process, the large deviation principle for the occupation measure conditioned not to exit a given subregion. The rate function vanis…