Analogs of renormalization group transformations in random processes

Michael F. Shlesinger and Barry D. Hughes

Physica A: Statistical Mechanics and its Applications, 1981, vol. 109, issue 3, 597-608

Abstract: We review the properties of a real-space renormalization group transformation of the free energy, including the existence of oscillatory terms multiplying the non-analytic part of the free energy. We then construct stochastic processes which incorporate into probability distributions the features of the free energy scaling equation. (The essential information is obtainable from the scaling equation and a direct solution for a probability is not necessary.) These random processes are shown to be generated directly from Cantor sets. In a spatial representation, the ensuing random process exhibits a transition between Gaussian and fractal behavior. In the fractal regime, the trajectories will, in an average sense, form self-similar clusters. In a temporal representation, the random process exhibits a transition between an asymptotically constant renewal rate and fractal behavior. The fractal regime represents a frozen state with only transient effects allowed and is related to charge transport in glasses.

Date: 1981
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437181900157
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:109:y:1981:i:3:p:597-608

DOI: 10.1016/0378-4371(81)90015-7

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().