A random walk approach to Galton-Watson trees
An approach is discussed linking Galton-Watson trees with arbitrary offspring distributions to random walk excursions and bridges [this idea was used independently by \textit{J.-F. Le Gall} and \textit{Y. Le Jan}, Ann. Probab. 26, No. 1, 213-252 (1998; Zbl 0948.60071)]. Applying this approach the authors investigate Galton-Watson trees with binary, Poisson or geometric offspring distribution and reveal some connections to the Dirac, Bose-Einstein and Maxwell-Boltzmann statistics. They also analyze the structure of the subtree of all descendants of a randomly chosen individual of a tree conditioned to have fixed size \(n\), study the lines of ancestors and ladder points of a related random walk and use the established facts to construct Galton-Watson trees conditioned to survive a given number of generations.
scientific article; zbMATH DE number 1552709
scientific article