Transport on randomly evolving trees

Details Transport on randomly evolving trees Transport on randomly evolving trees

2005-11-08

arxiv.org/abs/cond-mat/0511194v1

Physics

Condensed Matter

Statistical Mechanics

16 pages, 8 figures, published in Phys. Rev. E 72, 051101 (2005)

Scientific paper

10.1103/PhysRevE.72.051101

The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to nodes. By using the method of the age-dependent branching processes we derive the joint distribution function of the number of living and dead nodes, and determine the correlation between these node numbers as a function of time. Also analyzed are the stochastic properties of the end-nodes; and the correlation between the numbers of living and dead end-nodes is shown to change its character suddenly at the very beginning of the evolution process. The survival probability of random trees is investigated and expressions are derived for this probability.

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