Maximal height statistics for 1/fα signals

G. Györgyi, N. R. Moloney, K. Ozogány, Z. Rácz

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

Numerical and analytical results are presented for the maximal relative height distribution of stationary periodic Gaussian signals (one-dimensional interfaces) displaying a 1/fα power spectrum. For 0≤α1 (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 α→ ∞ and, for large α, by perturbation expansion. Furthermore, using path integral techniques we derive a trace formula for the distribution function, valid for α=2n even integer. From the latter we extract the small argument asymptote of the distribution function whose analytic continuation to arbitrary α>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.

Original languageEnglish
Article number021123
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume75
Issue number2
DOIs
Publication statusPublished - Feb 28 2007

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Distribution Function
distribution functions
statistics
Statistics
Asymptote
asymptotes
Perturbation Expansion
Trace Formula
Analytic Continuation
Curvilinear integral
Power Spectrum
Roughness
integers
power spectra
Extremes
roughness
Valid
perturbation
expansion
Integer

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Maximal height statistics for 1/fα signals. / Györgyi, G.; Moloney, N. R.; Ozogány, K.; Rácz, Z.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 75, No. 2, 021123, 28.02.2007.

Research output: Contribution to journalArticle

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