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Paper IPM / P / 8390  


Abstract:  
We carry out an exact analysis of the average frequency
ν^{+}_{axi} in the direction xi of positiveslope crossing
of a given level x_{i} such that, h(x,t)−―h = α, of
growing surfaces in spatial dimension d. Here, h(x, t) is the
surface height at time t, and ―h is its mean value. We
analyze the problem when the surface growth dynamics is governed
by the KardarParisiZhang (KPZ) equation without surface tension,
in the time regime prior to appearance of cusp singularities
(sharp valleys), as well as in the random deposition (RD) model.
The total number N^{+} of such levelcrossings with positive
slope in all the directions is then shown to scale with time as
t^{d/2} for both the KPZ equation and the RD model.
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