Convergence in law of the maximum of nonlattice branching random walk

  title={Convergence in law of the maximum of nonlattice branching random walk},
  author={M. Bramson and J. Ding and O. Zeitouni},
  journal={arXiv: Probability},
  • M. Bramson, J. Ding, O. Zeitouni
  • Published 2014
  • Mathematics
  • arXiv: Probability
  • Let $\eta^*_n$ denote the maximum, at time $n$, of a nonlattice one-dimensional branching random walk $\eta_n$ possessing (enough) exponential moments. In a seminal paper, Aidekon demonstrated convergence of $\eta^*_n$ in law, after recentering, and gave a representation of the limit. We give here a shorter proof of this convergence by employing reasoning motivated by Bramson, Ding and Zeitouni. Instead of spine methods and a careful analysis of the renewal measure for killed random walks, our… CONTINUE READING
    35 Citations
    On the maximal displacement of subcritical branching random walks
    • 5
    • PDF
    On the Maximal Displacement of Near-critical Branching Random Walks
    • PDF
    The minimum of a branching random walk outside the boundary case
    • 8
    • PDF
    Limit law for the cover time of a random walk on a binary tree
    • 6
    • PDF
    Cover time for branching random walks on regular trees
    • PDF
    Branching random walk in the presence of a hard wall
    • 1
    • PDF


    Convergence in law of the minimum of a branching random walk
    • 179
    • Highly Influential
    • PDF
    Minimal displacement of branching random walk
    • 71
    A local limit theorem for random walks conditioned to stay positive
    • 41
    • Highly Influential
    • PDF
    A Conditional Limit Theorem for the Frontier of a Branching Brownian Motion
    • 115
    • Highly Influential
    • PDF
    Extreme values for two-dimensional discrete Gaussian free field
    • 35
    • PDF
    Large Deviations Techniques and Applications
    • 4,547
    • PDF
    The First Birth Problem for an Age-dependent Branching Process
    • 213
    An Introduction to Probability Theory and Its Applications, Volume II
    • 1,033
    • Highly Influential