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On normalized multiplicative cascades under strong disorder

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https://ir.library.oregonstate.edu/concern/articles/41687j89v

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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 β > βc 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.
  • This is the publisher’s final pdf. The published article is copyrighted by the author(s) and published by the Institute of Mathematical Statistics. The published article can be found at: http://ecp.ejpecp.org/index.
  • Keywords: Tree Polymer, Partition function, Strong disorder, Multiplicative cascade
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  • Dey, P. S., & Waymire, E. C. (2015). On normalized multiplicative cascades under strong disorder. Electronic Communications in Probability, 20, 1-13. doi:10.1214/ECP.v20-3936
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  • 20
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  • This work began when PD was a Simons Postdoctoral fellow at the Courant Institute of Mathematical Sciences, New York University, where EW was a visitor. EW is also partially supported by a grant DMS-1408947 from the National Science Foundation.
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file details WaymireEdwardMathematicsOnNormalizedMultiplicative.pdf 2017-07-25 Público Descargar