Branching Random Walks with One Particle Generation Center and Possible Absorption at Every Point

Two-Species Branching Annihilating Random Walks with One Offspring

The last decades have seen considerable efforts to understand nonequilibrium absorbing phase transitions from an active phase into an absorbing phase consisting of absorbing states [1]. Once the system is trapped into an absorbing state, it can never escape from the state. Various one dimensional lattice models exhibiting absorbing transitions have been studied, and most of them turn out to bel...

Branching Random Walks

We study a generalized branching random walk where particles breed at a rate which depends on the number of neighbouring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population survives without exploding. We construct a non trivial invariant measure for this case.

Branching Processes and Random Walks

Branching Random Walks on Graphs

We study a new distributed randomized information propagation mechanism in networks that we call a branching random walk (BRW). BRW is a generalization of the well-studied “standard” random walk which is a fundamental primitive useful in a wide variety of network applications ranging from token management and load balancing to search, routing, information propagation and gossip. BRW is paramete...

Minima in Branching Random Walks

Given a branching random walk, let Mn be the minimum position of any member of the n’th generation. We calculate EMn to within O(1) and prove exponential tail bounds for P {|Mn − EMn| > x}, under quite general conditions on the branching random walk. In particular, together with work of [8], our results fully characterize the possible behavior of EMn when the branching random walk has bounded b...