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

S. L. Narasimhan, Joseph A. Nathan, P. S. R. Krishna and K. P. N. Murthy Solid State Physics Division, Reactor Physics Design Division Bhabha Atomic Research Centre, Mumbai-400085, India. Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamilnadu, India. Abstract 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 coarsegraining process) does not necessarily imply that long-range correlations found in the latter would correspond to those of the former.