Phase transition in equilibrium fluctuations of symmetric slowed exclusion

Abstract

We analyze the equilibrium fluctuations of the density, current and tagged particle in symmetric exclusion with a slow bond. The system evolves in the one-dimensional lattice and the jump rate is everywhere equal to one except at the slow bond where it is $\alpha n^{-}\beta$, where $\alpha ,\beta \ge 0$ and $n$ is the scaling parameter. Depending on the regime of $\beta$, we find three different behaviors for the limiting fluctuations whose covariances are explicitly computed. In particular, for the critical value $\beta =1$, starting a tagged particle near the slow bond, we obtain a family of gaussian processes indexed in $\alpha$, interpolating a fractional brownian motion of Hurst exponent 1/4 and the degenerate process equal to zero.

published

References in corpus (5)

• Universality of KPZ equation
• On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion
• Hydrodynamic limit of gradient exclusion processes with conductances
• Hydrodynamic behavior of one dimensional subdiffusive exclusion processes with random conductances
• Phase transition of a Heat equation with Robin's boundary conditions and exclusion process

Cited by in corpus (13)

• Exclusion process with slow boundary
• Crossover to the stochastic Burgers equation for the WASEP with a slow bond
• Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics
• Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems
• Fluctuation limit for interacting diffusions with partial annihilations through membranes
• Moderate Deviations for the SSEP with a Slow Bond
• Hydrodynamic Limit for the SSEP with a Slow Membrane
• On energy solutions to stochastic Burgers equation
• Hydrodynamic limit of Exclusion Processes with slow boundaries on hypercubes
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Non-Stationary KPZ equation from ASEP with slow bonds
• Asymptotic behavior of density in the boundary-driven exclusion process on the Sierpinski gasket
• Occupation times of exclusion processes with conductances