We study branching SDEs with law-dependent immigration and their mean-field particle approximations. Under a dissipativity condition and sufficiently weak interaction, a uniform propagation-of-chaos bound in time of order $N^{-1/2}$ is established. On every fixed finite time horizon, the same order of propagation of chaos holds for arbitrary finite interaction strength. A two-stage scaling limit connects continuous-time discrete-state mean-field birth--death processes to interacting branching diffusions and then to the nonlinear equation. For a logistic mean-field diffusion we prove a sharp criterion for extinction/non-extinction, and further show that weak enough interaction strength is necessary for a uniform-in-time approximation.
We study a class of interacting diffusion particle systems with memory and their mean-field limit using coupling methods. We first establish quantitative propagation of chaos estimates for this class of models. Our first main result is a uniform-in-time propagation of chaos estimate, under a suitable contraction condit...
We study metastability and long-time propagation-of-chaos for mean-field interacting diffusions on the circle with multiple local free-energy minima. Working modulo rotations, we identify sharp exponential time scales for metastability and the validity and breakdown of the McKean-Vlasov approximation. Assuming finitely...
Can the transition from integrability to chaos be discontinuous? We show that it can, and that the resulting first-order dynamical transition coexists with critical slowing down. Using an analytically tractable confined random walk and a deterministic stadium-like billiard, we find a finite jump of the stationary diffu...
A. K. P. da Fonseca, Marcelo de Almeida Presotto, D. M. Oliveira et al.· 0 citations
We study a class of discrete-time interacting particle systems arising from mean-field coupled maps. We establish a Dobrushin-type estimate, a relative entropy estimate and Central Limit Theorem (CLT) type results for this class of systems. First we control the growth of the 1-Wasserstein distance between the empirical...
We investigate a discontinuous route from integrability to chaos using a confined stochastic random walk and a deterministic stadium-like billiard. In both systems, the stationary diffusive observable exhibits a finite jump at the transition: it vanishes at the unperturbed limit but approaches a finite, geometry-contro...
A. K. P. da Fonseca, Marcelo de Almeida Presotto, D. M. Oliveira et al.· 0 citations
We consider a gradient, speed-change, symmetric exclusion process on the discrete torus $T^d_n$, $d\le 3$, whose empirical measure evolves, on the diffusive scale, according to a non-linear parabolic equation. We prove that, starting from a sequence of initial states whose relative entropy with respect to the inhomogen...
Claudio Landim, Sunder Sethuraman· 0 citations
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