Polynucleotide evolution and branching processes

Polynucleotide evolution and branching processes.

Branching Processes and Applications

These are notes of a talk given at the probability student seminar in the Weizmann institute of science on September 2011. After introducing Galton-Watson branching process, we consider conditions for which the process survives forever and for which it has a binary tree as a subtree with the same root. As an application, Mandelbrot’s fractal percolation model is discussed.

Branching Processes

Galton-Watson processes were introduced by Francis Galton in 1889 as a simple mathematical model for the propagation of family names. They were reinvented by Leo Szilard in the late 1930s as models for the proliferation of free neutrons in a nuclear fission reaction. Generalizations of the extinction probability formulas that we shall derive below played a role in the calculation of the critica...

Branching Processes

The study of branching processes began in the 1840s with Irénée-Jules Bienaymé, a probabilist and statistician, and was advanced in the 1870s with the work of Reverend Henry William Watson, a clergyman and mathematician, and Francis Galton, a biometrician. In 1873, Galton sent a problem to the Educational Times regarding the survival of family names. When he did not receive a satisfactory answe...

Branching Processes

We introduce the basic theory of Galton-Watson branching processes, and the probabilistic tools needed to analyse them. The aim is to give a basic treatment of branching processes, including results on the limiting behaviour for subcritical, critical, and supercritical processes. We introduce just enough probabilistic theory to make the results rigourous, but avoid unnecessary technicalities as...