Joint statistics of random walk on Z1 and accumulation of visits

J. K. Percus, O. E. Percus

Research output: Contribution to journalArticlepeer-review


We obtain the joint distribution PN (X, K | Z) of the location X of a one-dimensional symmetric next neighbor random walk on the integer lattice, and the number of times the walk has visited a specified site Z. This distribution has a simple form in terms of the one variable distribution pN′ (X´), where N ´ = N − K and X´ is a function of X, K, andZ. The marginal distributions of X and K are obtained, as well as their diffusion scaling limits.

Original languageEnglish (US)
Pages (from-to)499-505
Number of pages7
JournalTheory of Probability and its Applications
Issue number3
StatePublished - 2017


  • Frequency of visits
  • Symmetric random walks
  • Walk on integer lattice
  • Walker visit number correlation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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