[Todos] Seminario de Probabilidad y Estadística Matemática.

[Pablo Groisman]

Seminario de Probabilidad y Estadística Matemática.

PROXIMO ENCUENTRO: Miércoles 13 de octubre, 10:30hs.
EXPOSITORA: Cristina Toninelli,  Laboratoire de Probabilités et
Modèles Aléatoires, Université Pierre et Marie Curie (Paris 6) and
Denis Diderot (Paris 7)
TITULO: Universality in one dimensional Hierarchical Coalescence Processes
LUGAR: Sala de Seminarios, Dpto. de Matemática, Pabellón 1, Cdad. Universitaria.

RESUMEN: Motivated by several models introduced in the physical
literature to study the non-equilibrium coarsening dynamics of
one-dimensional systems, we consider a large class of hierarchical
coalescence processes (HCP). An HCP consists of an infinite sequence
of coalescence processes: each process occurs in a different epoch
indexed by "n" and evolves for an infinite time and the evolution in
subsequent epochs are linked in such a way that the initial
distribution of epoch "n" coincides with the final distribution of
epoch "n-1". Inside each epoch the process evolves as follows.
Intervals whose length belongs to a certain epoch-dependent finite
range are active, i.e. they can incorporate their left or right
neighboring interval with quite general rates. We show that if the
initial distribution describes a renewal process such a property is
preserved at all later times and all future epochs. Furthermore the
distribution of certain rescaled variables, e.g. the domain length,
has a well defined and universal limiting behavior as "n" goes to
infiniy  independent of the details of the process (merging rates,
activity
ranges,...), thus accounting  for  the universality in the limiting
behavior of very different physical systems.

Estan todos invitados.


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