Publications [#243435] of Richard T. Durrett

Papers Published

1. Durrett, R, Maxima of branching random walks, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 62 no. 2 (June, 1983), pp. 165-170, Springer Nature America, Inc, ISSN 0044-3719 [doi]
   (last updated on 2024/04/18)

   Abstract:
   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 φ{symbol}(θ) = ∝ exp (θx)dF(x)<∞ for some θ>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 → ∞ and log (-x)F(x)→0 as x→-∞. In this case we find that there is a sequence of constants an, which grow exponentially, so that Ln/an converges weakly to a nondegenerate distribution. This result is in sharp contrast to the linear growth of Ln observed in the case φ{symbol}(θ)<∞. © 1983 Springer-Verlag.