Some problems on random intervals and annihilating particles. (English) Zbl 0297.60052

Particles perform independent random walks on the integers, and are annihilated if they cross paths or land at the same point. The problem is to determine whether the origin is hit infinitely often. The answer is shown to depend on the initial distribution of particles in accordance with a “log log law”. Several equivalent models are mentioned.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60G50 Sums of independent random variables; random walks
60C05 Combinatorial probability
Full Text: DOI