Super-tree random measures (Q1366735)

A random measure \(\nu\) is constructed as limiting state of a supercritical discrete time branching random walk in which particle mass and step size are rescaled geometrically in time. At least heuristically, the law of \(\nu\) is related to the distribution of a superprocess at a certain deterministic time. In the main part of the paper, the almost sure support properties of \(\nu\) (such as compact support, carrying dimension, or existence of a smooth density) are investigated subject to varying conditions on the characteristics of the branching random walk.