Multiscaling in Stochastic Fractals

P. L. Krapivsky and E. Ben-Naim

a simple kinetic model describing the formation of a stochastic Cantor set in arbitrary spatial dimension d. In one dimension, the model exhibits scaling asymptotic behavior. For d>1, the volume distribution is characterized by a single scale $t^{-1/2}$, while other geometric properties such as the length are characterized by an infinite number of length scales and thus exhibit multiscaling.


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