48 citations · 162 across the 17 of their papers we have counts for
10 papers · 1 filter
On the action of multiplicative cascades on measures
Julien Barral, Xiong Jin
We consider the action of Mandelbrot multiplicative cascades on probability measures supported on a symbolic space. For general probability measures, we obtain almost a sharp crite…
Spectral representation of one-dimensional Liouville Brownian Motion and Liouville Brownian excursion
Xiong Jin
In this paper we apply the spectral theory of linear diffusions to study the one-dimensional Liouville Brownian Motion and Liouville Brownian excursions from a given point. As an a…
Exact dimensionality and projection properties of Gaussian multiplicative chaos measures
Kenneth Falconer, Xiong Jin
Given a measure on a regular planar domain , the Gaussian multiplicative chaos measure of studied in this paper is the random measure obtained as the li…
Dimension conservation for self-similar sets and fractal percolation
Kenneth Falconer, Xiong Jin
We introduce a technique that uses projection properties of fractal percolation to establish dimension conservation results for sections of deterministic self-similar sets. For exa…
On exact scaling log-Infinitely divisible cascades
Julien Barral, Xiong Jin
In this paper we extend some classical results valid for canonical multiplicative cascades to exact scaling log-infinitely divisible cascades. We complete previous results on non-d…
Gaussian multiplicative chaos and KPZ duality
Julien Barral, Xiong Jin, Rémi Rhodes +1
This paper is concerned with the construction of atomic Gaussian multiplicative chaos and the KPZ formula in Liouville quantum gravity. On the first hand, we construct purely atomi…
Dimension result and KPZ formula for two-dimensional multiplicative cascade processes
Xiong Jin
We prove a Hausdorff dimension result for the image of two-dimensional multiplicative cascade processes, and we obtain from this result a KPZ-type formula which normally has one po…
The graph, range and level set singularity spectra of -adic independent cascade function
Xiong Jin
With the "iso-Hölder" sets of a function we naturally associate subsets of the graph, range and level set of the function. We compute the associated singularity spectra for a class…
Convergence of complex multiplicative cascades
Julien Barral, Xiong Jin, Beno\^{ı}t Mandelbrot
The familiar cascade measures are sequences of random positive measures obtained on via -adic independent cascades. To generalize them, this paper allows the random weig…
Uniform convergence for complex -martingales
Julien Barral, Xiong Jin, Benoît Mandelbrot
Positive -martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their…