Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs

Details Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs

2011-10-13

arxiv.org/abs/1110.3012v1

Mathematics

Probability

Scientific paper

We consider the nonlinear stochastic heat equation in one dimension. Under
some conditions on the nonlinearity, we show that the "peaks" of the solution
are rare, almost fractal like. We also provide an upper bound on the length of
the "islands," the regions of large values. These results are obtained by
analyzing the correlation length of the solution.

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