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math.PR2025
Microcanonical cascades and random homeomorphisms
Xinxin Chen, Yong Han, Yanqi Qiu +1
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 regul…
math.PR2024★ 2 cited
Harmonic analysis of Mandelbrot cascades -- in the context of vector-valued martingales
Xinxin Chen, Yong Han, Yanqi Qiu +1
We solve a long-standing open problem of determining the Fourier dimension of the Mandelbrot canonical cascade measure (MCCM). This problem of significant interest was raised by Ma…
math.PR2023
Moments of Mandelbrot cascades at critical exponents
Yong Han, Yanqi Qiu, Zipeng Wang
We obtain the asymptotic growth rate of the moments of the Mandelbrot random cascades at critical exponents. The key ingredient is a to reduction method for the moment-es…