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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Independent random cascades on Galton-Watson trees


Authors: Gregory A. Burd and Edward C. Waymire
Journal: Proc. Amer. Math. Soc. 128 (2000), 2753-2761
MSC (2000): Primary 60G57, 60G30, 60G42; Secondary 60K35
Published electronically: March 1, 2000
MathSciNet review: 1657774
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Abstract: Consider an independent random cascade acting on the positive Borel measures defined on the boundary of a Galton-Watson tree. Assuming an offspring distribution with finite moments of all orders, J. Peyrière computed the fine scale structure of an independent random cascade on Galton-Watson trees. In this paper we use developments in the cascade theory to relax and clarify the moment assumptions on the offspring distribution. Moreover a larger class of initial measures is covered and, as a result, it is shown that it is the Hölder exponent of the initial measure which is the critical parameter in the Peyrière theory.


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Additional Information

Gregory A. Burd
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Address at time of publication: Marvell Semiconductor, Inc., 645 Almanor Avenue, Sunnyvale, California 94086
Email: burd@math.washington.edu, gburd@marvell.com

Edward C. Waymire
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331-4605
Email: waymire@math.orst.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05279-5
PII: S 0002-9939(00)05279-5
Received by editor(s): May 14, 1998
Received by editor(s) in revised form: October 8, 1998
Published electronically: March 1, 2000
Communicated by: Stanley Sawyer
Article copyright: © Copyright 2000 American Mathematical Society