Journal of Statistical Physics

, Volume 73, Issue 3, pp 625–641

Tree-based models for random distribution of mass


  • David Aldous
    • Department of StatisticsUniversity of California

DOI: 10.1007/BF01054343

Cite this article as:
Aldous, D. J Stat Phys (1993) 73: 625. doi:10.1007/BF01054343


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.

Key words

Spatial distributionrandom treesuper Brownian processlarge deviationsrecursive self-similarity

Copyright information

© Plenum Publishing Corporation 1993