28,783 research outputs found
A Sampling Theorem for Rotation Numbers of Linear Processes in
We prove an ergodic theorem for the rotation number of the composition of a
sequence os stationary random homeomorphisms in . In particular, the
concept of rotation number of a matrix can be generalized
to a product of a sequence of stationary random matrices in .
In this particular case this result provides a counter-part of the Osseledec's
multiplicative ergodic theorem which guarantees the existence of Lyapunov
exponents. A random sampling theorem is then proved to show that the concept we
propose is consistent by discretization in time with the rotation number of
continuous linear processes on ${\R}^{2}.
Spatial survival probability for one-dimensional fluctuating interfaces in the steady state
We report numerical and analytic results for the spatial survival probability
for fluctuating one-dimensional interfaces with Edwards-Wilkinson or
Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are
obtained from analysis of steady-state profiles generated by integrating a
spatially discretized form of the Edwards-Wilkinson equation to long times. We
show that the survival probability exhibits scaling behavior in its dependence
on the system size and the `sampling interval' used in the measurement for both
`steady-state' and `finite' initial conditions. Analytic results for the
scaling functions are obtained from a path-integral treatment of a formulation
of the problem in terms of one-dimensional Brownian motion. A `deterministic
approximation' is used to obtain closed-form expressions for survival
probabilities from the formally exact analytic treatment. The resulting
approximate analytic results provide a fairly good description of the numerical
data.Comment: RevTeX4, 21 pages, 8 .eps figures, changes in sections IIIB and IIIC
and in Figs 7 and 8, version to be published in Physical Review
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