Branching Processes in Random Trees

1 online resource (47 pages) : PDF

2012

University of North Carolina at Charlotte

We study the behavior of branching process in a random environment on trees in the critical, subcritical and supercritical case. We are interested in the case when both the branching and the step transition parameters are random quantities. We present quenched and annealed classifications for such processes and determine some limit theorems in the supercritical quenched case. Corollaries cover the percolation problem on random trees. The main tool is the compositions of random generating functions.

doctoral dissertations

Mathematics

Ph.D.

Branching Process
Galton-Watson Process
Percolation
Random Environment
Random Generating Functions

Applied Mathematics

Molchanov, Stanislav

Sonin, Isaac
Grabchak, Michael
Latulipe, Celine

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2012.

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Jutmaan_uncc_0694D_10361

http://hdl.handle.net/20.500.13093/etd:584