Microcanonical cascades and random homeomorphisms
Xinxin Chen, Yong Han, Yanqi Qiu, Zipeng Wang
TL;DR
This paper solves the Mandelbrot-Kahane problem for microcanonical cascade measures by determining their Fourier dimensions and explores properties like Frostman regularity and bi-Hölder continuity of related random homeomorphisms.
Contribution
It provides a complete solution to the Mandelbrot-Kahane problem for microcanonical cascade measures and analyzes their Fourier dimensions and regularity properties.
Findings
Exact Fourier dimensions of microcanonical cascade measures determined
Frostman regularity of the measures discussed
Bi-Hölder continuity of Dubins-Freedman random homeomorphisms analyzed
Abstract
We give a complete solution to the Mandelbrot-Kahane problem for the microcanonical cascade measures by determing their exact Fourier dimensions. We also discuss the Frostman regularity as well as the bi-H\"older continuity of the Dubins-Freedman random homeomorphisms.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Statistical Mechanics and Entropy · Theoretical and Computational Physics