 96159 Timo Seppalainen
 Hydrodynamic Scaling, Convex Duality, and Asymptotic
Shapes of Growth Models
(82K, AMSTeX)
Apr 29, 96

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Abstract. We present a technique for simultaneously deriving two related results:
Hydrodynamic scaling limits for onedimensional asymmetric particle
systems and asymptotic shapes for growth models. The idea is to specify
the particle dynamics in terms of a microscopic LaxOleinik formula
which leads directly to the macroscopic description in terms of a
nonlinear conservation law. The law of large numbers required for
this link comes from the growth model that is embedded in the particle
system. In the limit, the asymptotic shape of the growth model becomes
the convex conjugate of the flux of the conservation law, and the latter
is computable from the particle system in equilibrium. The asymptotic shape
is then obtained from the duality relation. The method is illustrated
with four applications.
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