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The Hausdorff dimension of pulse-sum graphs

Published online by Cambridge University Press:  01 July 2007

YANN DEMICHEL  and
KENNETH FALCONER
YANN DEMICHEL
Affiliation:
Department of Mathematics, University Blaise Pascal, 63177 Aubière Cedex, France. e-mail: [email protected]
KENNETH FALCONER
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews, Fife KY16 9SS. e-mail: [email protected]
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Abstract

We consider random functions formed as sums of pulseswhere Xn are independent random vectors, 0<α<1, and G is an elementary “pulse” or “bump”. Typically such functions have fractal graphs and we find the Hausdorff dimension of these graphs using a novel variant on the potential theoretic method.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 1 , July 2007 , pp. 145 - 155
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

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