Math @ Duke

Publications [#243435] of Richard T. Durrett
Papers Published
 Durrett, R, Maxima of branching random walks,
Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete, vol. 62 no. 2
(1983),
pp. 165170, ISSN 00443719 [doi]
(last updated on 2018/10/23)
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 1F(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 SpringerVerlag.


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