Probability distribution of the maximum of a smooth temporal signal

Details Probability distribution of the maximum of a smooth temporal signal Probability distribution of the maximum of a smooth temporal signal

2006-06-06

arxiv.org/abs/cond-mat/0606145v2

Phys. Rev. Lett. 98, 020601 (2007)

Physics

Condensed Matter

Statistical Mechanics

Final version (1 major typo corrected; better introduction). Accepted in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.98.020601

We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated to the probability that the process remains below a non-zero level M. When X(t) is a Gaussian process, our results are expressed explicitly in terms of the two-time correlation function, f(t)=.

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