Maximal height statistics for 1/f^alpha signals

Details Maximal height statistics for 1/f^alpha signals Maximal height statistics for 1/f^alpha signals

2006-10-17

arxiv.org/abs/cond-mat/0610463v1

Physics

Condensed Matter

Statistical Mechanics

17 pages, 8 figures, RevTex4

Scientific paper

Numerical and analytical results are presented for the maximal relative height distribution of stationary periodic Gaussian signals (one dimensional interfaces) displaying a 1/f^alpha power spectrum. For 01 (regime of strong correlations) and a highly accurate picture gallery of distribution functions can be constructed numerically. Analytical results can be obtained in the limit alpha -> infinity and, for large alpha, by perturbation expansion. Furthermore, using path integral techniques we derive a trace formula for the distribution function, valid for alpha=2n even integer. From the latter we extract the small argument asymptote of the distribution function whose analytic continuation to arbitrary alpha > 1 is found to be in agreement with simulations. Comparison of the extreme and roughness statistics of the interfaces reveals similarities in both the small and large argument asymptotes of the distribution functions.

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