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A branched chain approach to fractal time

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  • Ovidiu Vlad, Marcel

Abstract

A branched chain description of fractal time is suggested. Within its framework the long time tails are the result of a stochastic renormalization procedure. The jumps are grouped into blocks of random size, the blocks of blocks, etc., the size of a block being described by a branching chain process. The block formation ends up after a random number of steps, according to a scale invariant probability law. The general scaled form of a multi-state waiting time density function is derived. As expected, this function has a long tail for large times. The Shlesinger-Hughes time scaling (Physica A 109 (1981) 597) is recovered as a particular case of our approach. The fluctuation analysis outlines an essential feature of the theory: due to jump clustering, the correlation functions have also long tails; however, unlike the case of true chain reactions the system has the tendency to smooth the fluctuations.

Suggested Citation

  • Ovidiu Vlad, Marcel, 1992. "A branched chain approach to fractal time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 184(3), pages 325-341.
    • Handle: RePEc:eee:phsmap:v:184:y:1992:i:3:p:325-341
    DOI: 10.1016/0378-4371(92)90309-E
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    Cited by:

    1. Vlad, Marcel Ovidiu & Mackey, Michael C., 1996. "Industrial replacement, communication networks and fractal time statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 229(3), pages 295-311.

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