Laboratoire de Probabilités, Statistique et Modélisation

Cutoff phenomenon for asymmetric zero range process with monotone rates

We investigate the mixing time of the asymmetric Zero Range process on the segment with a nondecreasing rate. We establish that the cutoff holds in the totally asymmetric case with a convex flux, and also with a concave flux if the asymmetry is strong enough. We show that the mix...

Local stability and rates of convergence to equilibrium for the nonlinear renewal equation; applications to Hawkes processes

Abstract We study the asymptotic properties of the solutions of a nonlinear renewal equation. The main contribution of the present article is to provide stability and convergence results around equilibrium solutions, under some local subcritical condition. Quantitative rates of c...

Near-Critical Ornstein–Zernike Theory for the Planar Random-Cluster Model

Abstract We develop an Ornstein–Zernike theory for the two-dimensional random-cluster model with $$1 \le q <4$$ 1 ≤ q < 4 that also applies in its near-critical regime. In particular, we prove an asymptotic formula for the two-point function which holds uniformly for $$p < p_c$$...

Adaptive multilevel stochastic approximation of the value-at-risk

Crépey, Frikha and Louzi (Finance Stoch. (2025) 1015–1074) introduced a multilevel stochastic approximation scheme to compute the value-at-risk of a financial loss that is only simulatable by Monte Carlo. The best complexity of the scheme is in O(ε−52), ε>0 being a prescribed acc...