arXiv subjects

Maria Chiara Ricciuti

Publications and source records attributed to Maria Chiara Ricciuti.

4 recordsLinked to original sources

arXiv2026

Fluctuations of the Boundary-Driven Symmetric Zero-Range Process from the NESS

We study the non-equilibrium stationary fluctuations of a symmetric zero-range process on the discrete interval $\{1, \ldots, N-1\}$ coupled to reservoirs at sites $1$ and $N-1$, which inject and remove particles at rates proportional to $N^{-θ}$ for any value of $θ\in\mathbb{R}$. We prove that, if the jump rate is bounded and under diffusive scaling, the fluctuations converge to the solution of a generalised Ornstein-Uhlenbeck equation with characteristic operators that depend on the stationary density profile. The limiting equation is supplemented with boundary conditions of Dirichlet, Robin, or Neumann type, depending on the strength of the reservoirs. We also introduce two notions of solutions to the corresponding martingale problems, which differ according to the choice of test functions.

math.PR↗

arXiv2025

Scaling Limits of a Weakly Perturbed Random Interface Model

We consider a random interface model on the discrete torus with $2n$ sites, obtained from the classical corner flip dynamics but with a weak global perturbation, namely an asymmetry of order $n^{-γ}$ of the direction of growth that switches direction based on the sign of the total area under the interface. The slopes of this model can be viewed as a non-simple exclusion process at half filling with globally dependent rates. We show that, for $γ=1$, the hydrodynamic equation of the empirical density is given by a time concatenation of the viscous Burgers equation and the heat equation. Moreover, for $n$ prime and $γ>\frac{6}{7}$, we establish convergence in law of the equilibrium fluctuations to an infinite-dimensional Ornstein-Uhlenbeck process.

math.PR↗

arXiv2025

Stochastic Burgers Equation from Non-Product Stationary Measures via a Generalised Second-Order Boltzmann-Gibbs Principle

We prove a generalised second-order Boltzmann-Gibbs principle for conservative interacting particle systems on a lattice whose stationary measures are not of product type and not invariant under particle jumps. The result, which requires neither a spectral gap bound nor an equivalence of ensembles, extends the classical framework to settings with correlated invariant measures and is based on quantitative bounds for the correlation decay. As an application, we show that the equilibrium density fluctuations of the Katz-Lebowitz-Spohn model with a given choice of parameters converge, under diffusive scaling, to the stationary energy solution of the stochastic Burgers equation.

math.PR↗

arXiv2025

Hydrodynamic Limit of the Symmetric Zero-Range Process with Slow Boundary

We study the hydrodynamic behaviour of the symmetric zero-range process on the finite interval $\{1, \ldots, N-1\}$ in contact with slow reservoirs at the boundary. Particles are injected and removed at sites $1$ and $N-1$ at rates that scale like $N^{-θ}$ with $θ\ge1$. Under mild assumptions on the jump rate and the sequence of initial measures, we show that the empirical density evolves on the diffusive scale according to a nonlinear heat equation, with boundary conditions reflecting the strength of the reservoirs.

math.PR↗