Maxima of Branching Random Walks
نویسندگان
چکیده
In recent years several authors have obtained limit theorems for Ln, the location of the rightmost particle in a supercritical branching random walk but all of these results have been proved under the assumption that the offspring distribution has (p(O)=.fexp(Ox)dF(x)0. In this paper we investigate what happens when there is a slowly varying function K so that 1-F(x)~x-qK(x) as x ~ o o and log(x) F(x)~O as x , o o . In this case we find that there is a sequence of constants a N, which grow exponentially, so that L,/a,, converges weakly to a nondegenerate distribution. This result is in sharp contrast to the linear growth of L, observed in the case (p(0) < oo.
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