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Ehrhardt GC, Bray AJ. Series expansion calculation of persistence exponents. Phys Rev Lett. 2002;88(7):070601doi: 10.1103/PhysRevLett.88.070601.
Ehrhardt, G. C., & Bray, A. J. (2002). Series expansion calculation of persistence exponents. Physical review letters, 88(7), 070601. https://doi.org/10.1103/PhysRevLett.88.070601
Ehrhardt, George C M A, and Bray, Alan J. "Series expansion calculation of persistence exponents." Physical review letters vol. 88,7 (2002): 070601. doi: https://doi.org/10.1103/PhysRevLett.88.070601
Ehrhardt GC, Bray AJ. Series expansion calculation of persistence exponents. Phys Rev Lett. 2002 Feb 18;88(7):070601. doi: 10.1103/PhysRevLett.88.070601. Epub 2002 Jan 30. PMID: 11863878.
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Phys Rev Lett. 2002 Feb 18;88(7):070601. doi: 10.1103/PhysRevLett.88.070601. Epub 2002 Jan 30.

Series expansion calculation of persistence exponents.

Physical review letters

George C M A Ehrhardt, Alan J Bray

Affiliations

  1. Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.

PMID: 11863878 DOI: 10.1103/PhysRevLett.88.070601

Abstract

We consider an arbitrary Gaussian stationary process X(T) with known correlator C(T), sampled at discrete times Tn = nDeltaT. The probability that (n+1) consecutive values of X have the same sign decays as Pn approximately exp(-theta(D)Tn). We calculate the discrete persistence exponent theta(D) as a series expansion in the correlator C(DeltaT) up to fourteenth order, and extrapolate to DeltaT = 0 using constrained Padé approximants to obtain the continuum persistence exponent thetas. For the diffusion equation our results are in exceptionally good agreement with recent numerical estimates.

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