A formalism for studying long-range correlations in many-alphabets sequences

Details A formalism for studying long-range correlations in many-alphabets sequences A formalism for studying long-range correlations in many-alphabets sequences

2004-09-02

arxiv.org/abs/cond-mat/0409053v4

Physics

Condensed Matter

Statistical Mechanics

A clarifying note added in the introduction and in the summary; 13 pages including 3 figure

Scientific paper

We formulate a mean-field-like theory of long-range correlated $L$-alphabets sequences, which are actually systems with $(L-1)$ independent parameters. Depending on the values of these parameters, the variance on the average number of any given symbol in the sequence shows a linear or a superlinear dependence on the total length of the sequence. We present exact solution to the four-alphabets and three-alphabets sequences. We also demonstrate that a mapping of the given sequence into a smaller alphabets sequence (namely, a {\it coarse-graining} process) does not necessarily imply that long-range correlations found in the latter would correspond to those of the former.

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