96 citations · 158 across the 65 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…
Boundedness of Gaussian random sums on trees
Yong Han, Yanqi Qiu, Zipeng Wang
Let be a rooted tree endowed with the natural partial order . Let be a sequence of independent standard Gaussian random variables…
A note on the GFF with one free boundary condition
Yong Han, Yuefei Wang, Zipeng Wang
In this note, we shall prove an explicit formula on the probability of the level line of the Gaussian Free Field (GFF) with mixed boundary condition terminating at the free boundar…
On a class of random sets of positive integers
Yong Han, Yanqi Qiu, Zipeng Wang
In this note, we study a class of random subsets of positive integers induced by Bernoulli random variables. We obtain sufficient conditions such that the random set is almost sure…
Hyper-positive definite functions I: scalar case, branching-type stationary stochastic processes
Yanqi Qiu, Zipeng Wang
We propose a definition of branching-type stationary stochastic processes on rooted trees and related definitions of hyper-positivity for functions on the unit circle and functions…