### 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 language | English |
---|---|

Article number | 021123 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 75 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 28 2007 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*75*(2), [021123]. https://doi.org/10.1103/PhysRevE.75.021123

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

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 75, no. 2, 021123. https://doi.org/10.1103/PhysRevE.75.021123

}

TY - JOUR

T1 - Maximal height statistics for 1/fα signals

AU - Györgyi, G.

AU - Moloney, N. R.

AU - Ozogány, K.

AU - Rácz, Z.

PY - 2007/2/28

Y1 - 2007/2/28

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33847640684&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847640684&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.75.021123

DO - 10.1103/PhysRevE.75.021123

M3 - Article

AN - SCOPUS:33847640684

VL - 75

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 2

M1 - 021123

ER -