Thick and thin points for random recursive fractals
Thick and thin points for random recursive fractals
We consider random recursive fractals and prove fine results about their local behaviour. We show that for a class of random recursive fractals the usual multifractal spectrum is trivial in that all points have the same local dimension. However, by examining the local behaviour of the measure at typical points in the set, we establish the size of fine fluctuations in the measure. The results are proved using a large deviation principle for a class of general branching processes which extends the known large deviation estimates for the supercritical Galton-Watson process.
general branching process, large deviations, local dimension
251-277
Hambly, B.M.
953396cd-aad7-4dee-8a16-af59a067eff2
Jones, O.D.
d5046a34-1cd1-4404-95be-39fa10adc806
2003
Hambly, B.M.
953396cd-aad7-4dee-8a16-af59a067eff2
Jones, O.D.
d5046a34-1cd1-4404-95be-39fa10adc806
Hambly, B.M. and Jones, O.D.
(2003)
Thick and thin points for random recursive fractals.
Advances in Applied Probability, 35 (1), .
(doi:10.1239/aap/1046366108).
Abstract
We consider random recursive fractals and prove fine results about their local behaviour. We show that for a class of random recursive fractals the usual multifractal spectrum is trivial in that all points have the same local dimension. However, by examining the local behaviour of the measure at typical points in the set, we establish the size of fine fluctuations in the measure. The results are proved using a large deviation principle for a class of general branching processes which extends the known large deviation estimates for the supercritical Galton-Watson process.
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Published date: 2003
Keywords:
general branching process, large deviations, local dimension
Organisations:
Operational Research
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Local EPrints ID: 29687
URI: http://eprints.soton.ac.uk/id/eprint/29687
PURE UUID: 7f208b9e-c85b-4160-8b20-2301889dd364
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Date deposited: 12 May 2006
Last modified: 15 Mar 2024 07:33
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Author:
B.M. Hambly
Author:
O.D. Jones
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