Maxima of branching random walks


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Durrett, R

Published Date

  • June 1, 1983

Published In

Volume / Issue

  • 62 / 2

Start / End Page

  • 165 - 170

Electronic International Standard Serial Number (EISSN)

  • 1432-2064

International Standard Serial Number (ISSN)

  • 0044-3719

Digital Object Identifier (DOI)

  • 10.1007/BF00538794

Citation Source

  • Scopus