Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 20 (2015), paper no. 32, 13 pp.
On normalized multiplicative cascades under strong disorder
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.
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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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