We study the phenomenon of internal avalanching within the context of recently proposed “Tetris” lattice models for granular media. We consider a packing of particles subjected to two different dynamics. In the first case, we arrest the system at different instances during an “aging”...

We consider the branching processes in random environment. In this paper, we deal with the case of environments which are chosen stationary and ergodic from the finite set of geometrical offspring distributions. We denote by Zn the population at the n-th generation. We show that the large...

In a rapidly growing population one expects that two individuals chosen at random from the nth generation are unlikely to be closely related if n is large. In this paper it is shown that for a broad class of rapidly growing populations this is not the case. For a Galton–Watson branching...

A new variant of a branching process is introduced, with sufficient conditions for it to persist and to die out. The model is applied to discuss the asymptotic stability of a new type of queuing process.

In a multitype (d types) supercritical positively regular Galton–Watson branching process, let {Xn,Xn−1,…,X0} denote the types of a randomly chosen (i.e., uniform distribution) individual from the nth generation and this individual’s n ancestors. It is shown here that this sequence...

The Multifractal Embedded Branching Process (MEBP) process and Canonical Embedded Branching Process (CEBP) process were introduced by Decrouez and Jones (2012). The CEBP is a process in which the crossings of dyadic intervals constitute a branching process. An MEBP process is defined as a...

В современном обществе информационные активы являются основным ресурсом и обеспечивают компаниям добавленную стоимость. Сложность и размеры ущерба,...