Series Expansion Calculation of Persistence Exponents

Details Series Expansion Calculation of Persistence Exponents Series Expansion Calculation of Persistence Exponents

2001-09-27

arxiv.org/abs/cond-mat/0109526v1

Phys. Rev. Lett. 88, 070601 (2002)

Physics

Condensed Matter

Statistical Mechanics

5 pages; 5 page appendix containing series coefficients

Scientific paper

10.1103/PhysRevLett.88.070601

We consider an arbitrary Gaussian Stationary Process X(T) with known correlator C(T), sampled at discrete times T_n = n \Delta T. The probability that (n+1) consecutive values of X have the same sign decays as P_n \sim \exp(-\theta_D T_n). We calculate the discrete persistence exponent \theta_D as a series expansion in the correlator C(\Delta T) up to 14th order, and extrapolate to \Delta T = 0 using constrained Pad\'e approximants to obtain the continuum persistence exponent \theta. For the diffusion equation our results are in exceptionally good agreement with recent numerical estimates.

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