Series Expansion Calculation of Persistence Exponents
Abstract
We consider an arbitrary Gaussian stationary process X(T) with known correlator C(T), sampled at discrete times T_{n} = n∆T. The probability that (n+1) consecutive values of X have the same sign decays as P_{n}~exp(θ_{D}T_{n}). We calculate the discrete persistence exponent θ_{D} as a series expansion in the correlator C(∆T) up to fourteenth order, and extrapolate to ∆T = 0 using constrained Padé approximants to obtain the continuum persistence exponent θ. For the diffusion equation our results are in exceptionally good agreement with recent numerical estimates.
 Publication:

Physical Review Letters
 Pub Date:
 February 2002
 DOI:
 10.1103/PhysRevLett.88.070601
 arXiv:
 arXiv:condmat/0109526
 Bibcode:
 2002PhRvL..88g0601E
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 5 pages