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

We formulate a mean-field-like theory of long-range correlated L  -alphabets sequences, which are actually systems with (L-1)(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 coarse-graining process) does not necessarily imply that long-range correlations found in the latter would correspond to those of the former.