Tightness for a family of recursion equations

Maury D Bramson, Ofer Zeitouni

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


In this paper we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the maximal displacement of a branching random walk in one dimension and the cover time of a symmetric simple random walk on regular binary trees. Recursion equations associated with the distribution functions of these quantities have been used to establish weak laws of large numbers. Here, we use these recursion equations to establish the tightness of the corresponding sequences of distribution functions after appropriate centering.We phrase our results in a fairly general context, which we hope will facilitate their application in other settings.

Original languageEnglish (US)
Pages (from-to)615-653
Number of pages39
JournalAnnals of Probability
Issue number2
StatePublished - Mar 2009


  • Branching random walk
  • Cover time
  • Recursion equations
  • Tightness


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