On the moments of some Mandelbrot cascades

We study the moment of some random variables arising from the Mandelbrot cascades on a quite general tree. By applying Burkholder inequalities and Burkholder-Rosenthal inequalities in this setting, we are able to compute the $p$-moments of these random variables up to a multiplicative constant depending only on the tree and $p$. As a consequence, we recover several results of Kahane and also of Aihua Fan on the the multiplicative chaos. This talk is based on a recent joint work with Yong Han and Zipeng Wang.