2004/09/02 by S. L. Narasimhan, Narasimhan, S. L., Joseph A. Nathan +5
Physics and Astronomy · #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0409053
A clarifying note added in the introduction and in the summary; 13 pages including 3 figure
arxiv created 2005/09/13 · arxiv updated 2009/12/01
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.