arXiv subjects

R. Marinho

Publications and source records attributed to R. Marinho.

2 recordsLinked to original sources

arXiv2022

CLT for NESS of a reaction-diffusion model

We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the NESS, with an explicit rate of convergence, and we also show that at mesoscopic scales the NESS is well approximated by a local equilibrium (product) measure, in the total variation distance. In addition, in dimensions $d \leq3$ we show a central limit theorem (CLT) for the density of particles under the NESS. The corresponding Gaussian limit can be represented as an independent sum of a white noise and a massive Gaussian free field, and in particular it presents macroscopic correlations.

math.PR↗

arXiv2022

Scaling limits for Rudvalis card shuffles

We consider the Rudvalis card shuffle and some of its variations that were introduced by Diaconis and Saloff-Coste in \cite{symmetrized}, and we project them to some stochastic interacting particle system. For the latter, we derive the hydrodynamic limits and we study the equilibrium fluctuations. Our results show that, for these shuffles, when we consider an asymmetric variation of the Rudvalis shuffle, the hydrodynamic limit in Eulerian scale is given in terms of a transport equation with a constant that depends on the exchange rates of the system; while for symmetric and weakly asymmetric variations of this shuffle, in diffusive time scale, the evolution is given by the solution of a martingale problem.

math.PR↗