Phase transition in equilibrium fluctuations of symmetric slowed exclusion

• Autor(a) principal: Franco, Tertuliano
• Data de Publicação: 2013
• Outros Autores: Gonçalves, Patrícia, Neumann, Adrian
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/24539
• topic: Equilibrium fluctuations; Slowed exclusion; Phase transition; Science & Technology

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.