Hambly, B. M. and Lapidus, M. L. (2003) Random fractal strings: their zeta functions, complex dimensions and spectral asymptotics. Transactions of the American Mathematical Society . (In Press)

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Abstract
In this paper a string is a sequence of positive nonincreasing real numbers which sums to one. For our purposes a fractal string is a string formed from the lengths of removed subintervals created by a recursive decomposition of the unit interval. By using the so called complex dimensions of the string, the poles of an associated zeta function, it is possible to obtain detailed information about the behaviour of the asymptotic properties of the string. We consider random versions of fractal strings. We show that using a random recursive selfsimilar construction it is possible to obtain similar results to those for deterministic selfsimilar strings. In the case of strings generated by the excursions of stable subordinators, we show that the complex dimensions can only lie on the real line. The results allow us to discuss the geometric and spectral asymptotics of onedimensional domains with random fractal boundary.
Item Type:  Article 

Subjects:  O  Z > Probability theory and stochastic processes 
Research Groups:  Stochastic Analysis Group Oxford Centre for Industrial and Applied Mathematics 
ID Code:  113 
Deposited By:  Ben Hambly 
Deposited On:  04 Aug 2004 
Last Modified:  29 May 2015 18:16 
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