Minimal displacement of branching random walk

Maury D. Bramson

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Let {Mathematical expression} denote a branching random walk in {Mathematical expression} with mean particle production m, m>1, and with incremental spatial distribution G, with G({0}) =p and G({1})=1-p. If mp=1, then the minimal displacement of {Mathematical expression} behaves asymptotically like log log n/log 2. If the condition G({1})=1-p is replaced by G((0, ∞))=1-p, we obtain a similar result.

Original languageEnglish (US)
Pages (from-to)89-108
Number of pages20
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Issue number2
StatePublished - Jun 1 1978


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