Can coarse-graining introduce long-range correlations in a symbolic sequence?S. L. Narasimhan1, J. A. Nathan2 and K. P. N. Murthy3
1 Solid State Physics Division, Bhabha Atomic Research Center Mumbai-400085, India
2 Reactor Physics Design Division, Bhabha Atomic Research Center Mumbai-400085, India
3 Materials Science Division, Indira Gandhi Center for Atomic Research, Kalpakkam 603102, Tamilnadu, India
received 28 April 2004; accepted in final form 29 October 2004
published online 10 December 2004
We present an exactly solvable mean-field-like theory of correlated ternary sequences which are actually systems with two independent parameters. Depending on the values of these parameters, the variance on the average number of any given symbol shows a linear or a superlinear dependence on the length of the sequence. We have shown that the available phase space of the system is made up of a diffusive region surrounded by a superdiffusive region. Motivated by the fact that the diffusive portion of the phase space is larger than that for the binary, we have studied the mapping between these two. We have identified the region of the ternary phase space, particularly the diffusive part, that gets mapped into the superdiffusive regime of the binary. This exact mapping implies that long-range correlations found in a lower-dimensional representative sequence may not, in general, correspond to the correlation properties of the original system.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
02.50.Ga - Markov processes.
87.10.+e - Biological and medical physics: General theory and mathematical aspects.
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