8 papers
Finite reservoirs lead to Wentzell boundary conditions for independent random walks and exclusion process
Matheus Franco, Tertuliano Franco, Patrícia Gonçalves
We analyze the scaling limits (hydrodynamics/propagation of local equilibrium) of two particle systems, namely independent random walks (IRW) and symmetric exclusion processes (SEP…
Delayed logistic equation as a limit of long memory Markov chains
Eldon Barros, Dirk Erhard, Tertuliano Franco +1
We introduce and analyze a long-memory continuous-time Markov chain on whose jump mechanism depends explicitly on a state in the past. From the present state …
The Most General Brownian Motion on the Line and on Two Closed Half-Lines
Dirk Erhard, Tertuliano Franco, Wanessa Muricy
In the 1950s, W. Feller characterized the most general Brownian motion on the closed half-line. He showed that any such process is a mixture of reflected, sticky, and killed Browni…
Hydrodynamic limit for repeated averages on the complete graph
Alberto M. Campos, Tertuliano Franco, Markus Heydenreich +1
We establish a hydrodynamical limit for the averaging process on the complete graph with N vertices, showing that, after a timescale of order N, the empirical distribution of opini…
Superdiffusive Scaling Limits for the Symmetric Exclusion Process with Slow Bonds
Dirk Erhard, Tertuliano Franco, Tiecheng Xu
In \cite{fgn1}, the hydrodynamic limit in the diffusive scaling of the symmetric simple exclusion process with a finite number of slow bonds of strength has been studied.…
A strong large deviation principle for the empirical measure of random walks
Dirk Erhard, Tertuliano Franco, Joedson de Jesus Santana
In this article we show that the empirical measure of certain continuous time random walks satisfies a strong large deviation principle with respect to a topology introduced in~\ci…