SPDE Approximation for Random Trees

Details SPDE Approximation for Random Trees SPDE Approximation for Random Trees

2009-09-14

arxiv.org/abs/0909.2283v3

Mathematics

Probability

39 pages; 2 figure

Scientific paper

We consider the genealogy tree for a critical branching process conditioned on non-extinction. We enumerate vertices in each generation of the tree so that for each two generations one can define a monotone map describing the ancestor--descendant relation between their vertices. We show that under appropriate rescaling this family of monotone maps converges in distribution in a special topology to a limiting flow of discontinuous monotone maps which can be seen as a continuum tree. This flow is a solution of an SPDE with respect to a Brownian sheet.

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