## Electronic Communications in Probability

### On normalized multiplicative cascades under strong disorder

#### Abstract

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

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

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

https://projecteuclid.org/euclid.ecp/1465320959

Digital Object Identifier
doi:10.1214/ECP.v20-3936

Mathematical Reviews number (MathSciNet)
MR3327871

Zentralblatt MATH identifier
1321.60206

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

Rights

#### Citation

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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