Longest and heaviest paths in barak-erdos directed random graphs and related models

We analyze asymptotic properties (SLLN, FCLT, etc.) of paths of maximal length in a class of acyclic directed random graphs. For that, we need an auxiliary infinite bin model. Next, we introduce a perfect simulation algorithm for estimating the growth rate of maximal paths. Then we consider some generalizations of the model (edges have random weights, complete ordering is replaced by partial one, etc.) In a particular case of a parametric family of two-point distributions, we discuss amusing properties of (non)differentiability of the growth rate w.r. to the parameter. If time allows, we show how do Poisson forest, Tracy-Widom distribution and further exotics do appear in this setting. This is a joint work with Takis Konstantopoulos and several other authors. Подключение смотрите на сайте семинара: http://iitp.ru/ru/userpages/74/285.htm