Random Geometric Series

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dc.creatorBen-Naim, E.
dc.creatorKrapivsky, P. L.
dc.date2004-03-05
dc.date.accessioned2026-07-07T02:56:47Z
dc.date.available2026-07-07T02:56:47Z
dc.descriptionInteger sequences where each element is determined by a previous randomly chosen element are investigated analytically. In particular, the random geometric series x_n=2x_p with 0<=p<=n-1 is studied. At large n, the moments grow algebraically, <x_n^s> n^beta(s) with beta(s)=2^s-1, while the typical behavior is x_n n^ln 2. The probability distribution is obtained explicitly in terms of the Stirling numbers of the first kind and it approaches a log-normal distribution asymptotically.
dc.description6 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0403157
dc.identifierhttp://arxiv.org/abs/cond-mat/0403157
dc.identifierJ. Phys. A 37, 5949 (2004)
dc.identifierdoi:10.1088/0305-4470/37/23/001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/23464
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.subjectProbability
dc.titleRandom Geometric Series
dc.typetext

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