Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#243435] of Richard T. Durrett

Papers Published

  1. Durrett, R, Maxima of branching random walks, Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 62 no. 2 (1983), pp. 165-170, ISSN 0044-3719 [doi]
    (last updated on 2017/12/17)

    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.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320