The narrowest tube of a recurrent random walk

E. Csáki, A. Földes

Research output: Contribution to journalArticle

5 Citations (Scopus)


Let X1, X2, ... be i.i.d. random variables with P(X1=+1)=P(X1 =-1)=1/2. Put S0=0, Sn=X1+...+Xn (n≧1). Our aim is to investigate the a.s. behavior of {Mathematical expression} and {Mathematical expression}. It is shown that for aN=[c log N] both U(aN, N) and V(aN, N) are a.s. constant for large N, except for certain values of c, when U and V can take two values for large N. The result is extended for recurrent random walk too.

Original languageEnglish
Pages (from-to)387-405
Number of pages19
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Issue number3
Publication statusPublished - Sep 1 1984

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Mathematics(all)

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