Domination Between Trees and Application to an Explosion Problem

Details Domination Between Trees and Application to an Explosion Problem Domination Between Trees and Application to an Explosion Problem

2004-04-02

arxiv.org/abs/math/0404044v1

Ann. Probab., 22, 180--194 (1994)

Mathematics

Probability

22 pages

Scientific paper

We define a notion of stochastic domination between trees, where one tree dominates another if when the vertices of each are labeled with independent, identically distributed random variables, one tree is always more likely to contain a path with a specified property. Sufficient conditions for this kind of domination are (1) more symmetry and (2) earlier branching. We apply these conditions to the problem of determining how fast a tree must grow before first-passage percolation on the tree exhibits an explosion, that is to say, infinitely many vertices are reached in finite time. For a tree in which each vertex at distance n-1 from the root has f(n) offspring, f nondecreasing, an explosion occurs with exponentially distributed passage times if and only if sum f(n)^{-1}

Affiliated with

Also associated with

No associations

Rating

Domination Between Trees and Application to an Explosion Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Domination Between Trees and Application to an Explosion Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Domination Between Trees and Application to an Explosion Problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-287331