Speaker
Sergei Nechaev
(LPTMS Paris XI)
Description
We consider a (1 + 1)-dimensional ballistic deposition pro-
cess with next-nearest neighbor interaction, which belongs to
the KPZ universality class, and introduce for this discrete model
a variational formulation similar to that for the randomly forced
continuous Burgers equation. This allows to identify the
characteristic structures in the bulk of a growing aggregate
("clusters" and "crevices") with minimizers and shocks in the
Burgers turbulence. We find scaling laws that characterize the
ballistic deposition patterns in the bulk: the "thinning" of
the forest of clusters with increasing height, and the size
distribution of clusters. The corresponding critical exponents
are computed using the analogy with the Burgers turbulence.
