, Volume 73, Issue 3-4, pp 625-641

Tree-based models for random distribution of mass

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Abstract

A mathematical model for distribution of mass ind-dimensional space, based upon randomly embedding random trees into space, is introduced and studied. The model is a variant of thesuper Brownian motion process studied by mathematicians. We present calculations relating to (i) the distribution of position of a typical mass element, (ii) moments of the center of mass, (iii) large-deviation behavior, and (iv) a recursive self-similarity property.