On the Shape of the Wavefront of Branching Random Walk
We consider branching random walk on the integers with bounded steps, and study the position X n of the left-most particle at time n. The random variables (Xn — EXn) are uniformly tight. In the critical case there are uncountably many limitpoints. We shall explain the associated changing shape of the wavefront from the viewpoints of both weak and strong convergence. The question of whether these two methods lead to the same solution leads to some new near-constancy phenomena.
Unable to display preview. Download preview PDF.
- [KCG]Kuczma, M., Choczewski, B., and Ger, R. Iterative functional equations, Enc. Math. Appl. 32, Cambridge Univ. Press, Cambridge (1990).Google Scholar