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Multifractal Spectra of Fragmentation Processes

Abstract:

Let (S(t), t ≥ 0) be a homogeneous fragmentation of ]0, 1[ with no loss of mass. For x ∈ ]0, 1[, we say that the fragmentation speed of x is v if and only if, as time passes, the size of the fragment that contains x decays exponentially with rate v. We show that there is vtyp > 0 such that almost every point x ∈ ]0, 1[ has speed vtyp. Nonetheless, for v in a certain range, the random set script G signv, of points of speed v, is dense in ]0, 1[, and we compute explicitly the spectrum v → Di...

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Publisher copy:
10.1023/A:1026060516513

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Journal:
Journal of Statistical Physics
Volume:
113
Issue:
3-4
Pages:
411-430
Publication date:
2003-11-05
DOI:
ISSN:
0022-4715
URN:
uuid:2b5a160e-18fa-4048-b049-2c6178e43f83
Source identifiers:
487696
Local pid:
pubs:487696

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