[Todos] Seminario de Probabilidad y Estadística Matemática

[Pablo Groisman]

Seminario de Probabilidad y Estadística Matemática.

PROXIMO ENCUENTRO: Miércoles 6 de Julio, 12:00hs.
EXPOSITOR: Adriana Neumann, Universidade Federal do Rio Grande do Sul.
TITULO:  Large Deviations for the Exclusion Process with slow bond
LUGAR: Instituto de Cálculo, 2do piso, Pabellón 2.

RESUMEN: This talk is about the large deviations principle for the
symmetric simple exclusion process in non-homogeneous environments,
the non-homogeneity is due to the presence of slow bond. While an
usual bond has exchange rate one, a slow bond has a lower exchange
rate. This rate of passage of particles is called conductance. With
respect to the scaling  parameter, we assume that a slow bond has
conductance equal to 1 / N. The time-evolution of spatial density of
particles, usually called the empirical measure, converges under
diffusive scaling to a weak solution of the heat equation with Neumann
boundary conditions. This is called hydrodynamic limit and corresponds
to the law of large numbers for empirical measures of the
time-evolution of spatial density of particles. The equation mentioned
above is called the hydrodynamic equation. The boundary conditions
appear due to the presence of the slow bond. A natural question is the
rate which the empirical measure deviates from the hydrodynamic
profile, the so-called large deviations  principle. To get it in this
model we study the time-evolution of spatial density of particles in
conjunction with the density of particles that cross the slow bond.
This is a joint work with Tertuliano Franco and Claudio Landim.


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