Phase transition in equilibrium fluctuations of symmetric slowed exclusion

We analyze the equilibrium fluctuations of 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 $\alpha n^-\beta$, with $\alpha,\beta\geq{0}$ an...

ver descrição completa

Detalhes bibliográficos
Autor principal: Franco, Tertuliano (author)
Outros Autores: Gonçalves, Patrícia (author), Neumann, Adrian (author)
Formato: article
Idioma:eng
Publicado em: 2013
Assuntos:
Texto completo:http://hdl.handle.net/1822/24539
País:Portugal
Oai:oai:repositorium.sdum.uminho.pt:1822/24539
Descrição
Resumo:We analyze the equilibrium fluctuations of 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 $\alpha n^-\beta$, with $\alpha,\beta\geq{0}$ 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.