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We consider the symmetric simple exclusion process with slow boundary first introduced in [Baldasso {it et al.}, Journal of Statistical Physics, 167(5), 2017]. We prove a law of large number for the empirical measure of the process under a longer time scaling instead of the usual diffusive time scaling.
We consider the one dimensional symmetric simple exclusion process with a slow bond. In this model, particles cross each bond at rate $N^2$, except one particular bond, the slow bond, where the rate is $N$. Above, $N$ is the scaling parameter. This m
The TCP window size process appears in the modeling of the famous Transmission Control Protocol used for data transmission over the Internet. This continuous time Markov process takes its values in $[0,infty)$, is ergodic and irreversible. It belongs
We consider a velocity field with linear viscous interactions defined on a one dimensional lattice. Brownian baths with different parameters can be coupled to the boundary sites and to the bulk sites, determining different kinds of non-equilibrium st
We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that appear in
A fractional Ficks law and fractional hydrostatics for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities on the left and on the right are derived.