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”...

A natural sufficient condition is given for a Galton-Watson process in a varying environment to have a single rate of growth that obtains throughout the survival set of the process. In the homogeneous process the growth rate is provided by the usual Seneta-Heyde norming.

We study asymptotic properties of non-negative random variables Xn, n[greater-or-equal, slanted]0, satisfying the recursion . If the functions g(x) and [sigma]2(x) are properly balanced at infinity, Xn is asymptotically [Gamma]-distributed in a suitable scale. This result contains several known...

Let {Zn} be a supercritical Galton-Watson process in varying environments. It is known that Zn when normed by its mean EZn converges almost surely to a finite random variable W. It is possible, however, for such a process to exhibit more than one rate of growth so that in particular {W 0} need...

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.