Electronic Communications in Probability

On normalized multiplicative cascades under strong disorder

Partha Dey and Edward Waymire

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The purpose of this note is to provide a coupling of weak limits in distribution of sequence of (normalized) multiplicative cascade measures under strong disorder in terms of the extremes of an associated branching random walk, assuming i.i.d positive, non-lattice bond weights and a second moment condition. The solution is expressed as an almost sure coupling of random probability measures in the disorder parameter $\beta > \beta_c$ through the introduction of a tree-indexed random field of derivative martingales, and the Brunet-Derrida-Madaule decorated Poisson point process. A number of corollaries are provided to illustrate the utility of this construction.

Article information

Electron. Commun. Probab., Volume 20 (2015), paper no. 32, 13 pp.

Accepted: 1 April 2015
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G60: Random fields
Secondary: 60G57: Random measures 60G52: Stable processes

Multiplicative cascade tree polymer partition function strong disorder superposable derivative martingale

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Dey, Partha; Waymire, Edward. On normalized multiplicative cascades under strong disorder. Electron. Commun. Probab. 20 (2015), paper no. 32, 13 pp. doi:10.1214/ECP.v20-3936. https://projecteuclid.org/euclid.ecp/1465320959

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