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.
- 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