Abstract
We propose a non-Markovian extension of the L\'evy walk model of Shlesinger and Klafter [Phys. Rev. Lett. 54, 2551 (1985)], termed self-avoiding L\'evy walk, to study a polymer configuration having a broad persistance length distribution. We use the Flory-type argument in a manner analogous to the self-avoiding walk and the self-avoiding L\'evy flight schemes to include the excluded-volume effect and find that the Flory exponent ${\ensuremath{\nu}}_{\mathit{F}}$ varies continuously from the flexible limit [${\ensuremath{\nu}}_{\mathit{F}}$=3/(d+2)] to the stiff limit (${\ensuremath{\nu}}_{\mathit{F}}$=1), when the spatial dimension d and the L\'evy index \ensuremath{\mu} are varied. We also discuss the fractal dimensions and the morphology of L\'evy walks in comparison with the L\'evy flights.
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