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On the Shape of the Wavefront of Branching Random Walk

  • F. M. Dekking
  • E. R. Speer
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 84)

Abstract

We consider branching random walk on the integers with bounded steps, and study the position X n of the left-most particle at time n. The random variables (Xn — EXn) are uniformly tight. In the critical case there are uncountably many limitpoints. We shall explain the associated changing shape of the wavefront from the viewpoints of both weak and strong convergence. The question of whether these two methods lead to the same solution leads to some new near-constancy phenomena.

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • F. M. Dekking
    • 1
  • E. R. Speer
    • 2
    • 3
  1. 1.Thomas Stieltjes Institute of Mathematics and Department of Mathematics and Computer ScienceDelft University of TechnologyDelftThe Netherlands
  2. 2.Isaac Newton Institute for Mathematical SciencesCambridgeUK
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickNew JerseyUSA

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