### Abstract

Order statistics of periodic, Gaussian noise with 1/fα power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d _{k}= _{k}-x _{k+1}between the kth and (k+1)st largest values of the signal. The result d _{k}∼k ^{-}1, known for independent, identically distributed variables, remains valid for 0≤αk∼k ^{(}α ^{-}3 ^{)/}2, emerge for 1k∼k, is obtained for α>5. The spectra of average ordered values ε' _{k}= _{1}-x _{k}∼kβ is also examined. The exponent β is derived from the gap scaling as well as by relating ε' _{k} to the density of near-extreme states. Known results for the density of near-extreme states combined with scaling suggest that β(α=2)=1/2, β(4)=3/2, and β(∞)=2 are exact values. We also show that parallels can be drawn between ε' _{k} and the quantum mechanical spectra of a particle in power-law potentials.

Original language | English |
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Article number | 061101 |

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

Volume | 84 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 1 2011 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

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

*84*(6), [061101]. https://doi.org/10.1103/PhysRevE.84.061101

**Order statistics of 1/fα signals.** / Moloney, N. R.; Ozogány, K.; Rácz, Z.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 84, no. 6, 061101. https://doi.org/10.1103/PhysRevE.84.061101

}

TY - JOUR

T1 - Order statistics of 1/fα signals

AU - Moloney, N. R.

AU - Ozogány, K.

AU - Rácz, Z.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - Order statistics of periodic, Gaussian noise with 1/fα power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d k= k-x k+1between the kth and (k+1)st largest values of the signal. The result d k∼k -1, known for independent, identically distributed variables, remains valid for 0≤αk∼k (α -3 )/2, emerge for 1k∼k, is obtained for α>5. The spectra of average ordered values ε' k= 1-x k∼kβ is also examined. The exponent β is derived from the gap scaling as well as by relating ε' k to the density of near-extreme states. Known results for the density of near-extreme states combined with scaling suggest that β(α=2)=1/2, β(4)=3/2, and β(∞)=2 are exact values. We also show that parallels can be drawn between ε' k and the quantum mechanical spectra of a particle in power-law potentials.

AB - Order statistics of periodic, Gaussian noise with 1/fα power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d k= k-x k+1between the kth and (k+1)st largest values of the signal. The result d k∼k -1, known for independent, identically distributed variables, remains valid for 0≤αk∼k (α -3 )/2, emerge for 1k∼k, is obtained for α>5. The spectra of average ordered values ε' k= 1-x k∼kβ is also examined. The exponent β is derived from the gap scaling as well as by relating ε' k to the density of near-extreme states. Known results for the density of near-extreme states combined with scaling suggest that β(α=2)=1/2, β(4)=3/2, and β(∞)=2 are exact values. We also show that parallels can be drawn between ε' k and the quantum mechanical spectra of a particle in power-law potentials.

UR - http://www.scopus.com/inward/record.url?scp=84555187583&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84555187583&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.84.061101

DO - 10.1103/PhysRevE.84.061101

M3 - Article

C2 - 22304034

AN - SCOPUS:84555187583

VL - 84

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 6

M1 - 061101

ER -