A Theory of Intermittency Differentiation of 1D Infinitely Divisible Multiplicative Chaos Measures

A Theory of Intermittency Differentiation of 1D Infinitely Divisible Multiplicative Chaos Measures A theory of intermittency differentiation is developed for a general class of 1D infinitely divisible multiplicative chaos measures. The intermittency invariance of the underlying infinitely divisible field is established and utilized to derive a Feynman–Kac equation for the distribution of the total mass of the limit measure by considering a stochastic flow in intermittency. The resulting equation prescribes the rule of intermittency differentiation for a general functional of the total mass and determines the distribution of the total mass and its dependence structure to the first order in intermittency. A class of non-local functionals of the limit measure extending the total mass is introduced and shown to be invariant under intermittency differentiation making the computation of the full high-temperature expansion of the total mass distribution possible in principle. For application, positive integer moments and covariance structure of the total mass are considered in detail. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales Henri Poincaré Springer Journals

A Theory of Intermittency Differentiation of 1D Infinitely Divisible Multiplicative Chaos Measures

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Dynamical Systems and Ergodic Theory; Quantum Physics; Mathematical Methods in Physics; Classical and Quantum Gravitation, Relativity Theory; Elementary Particles, Quantum Field Theory
ISSN
1424-0637
eISSN
1424-0661
D.O.I.
10.1007/s00023-018-0656-8
Publisher site
See Article on Publisher Site

Abstract

A theory of intermittency differentiation is developed for a general class of 1D infinitely divisible multiplicative chaos measures. The intermittency invariance of the underlying infinitely divisible field is established and utilized to derive a Feynman–Kac equation for the distribution of the total mass of the limit measure by considering a stochastic flow in intermittency. The resulting equation prescribes the rule of intermittency differentiation for a general functional of the total mass and determines the distribution of the total mass and its dependence structure to the first order in intermittency. A class of non-local functionals of the limit measure extending the total mass is introduced and shown to be invariant under intermittency differentiation making the computation of the full high-temperature expansion of the total mass distribution possible in principle. For application, positive integer moments and covariance structure of the total mass are considered in detail.

Journal

Annales Henri PoincaréSpringer Journals

Published: Feb 19, 2018

References

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