Recurrence and Polya number of general one-dimensional random walks

Details Recurrence and Polya number of general one-dimensional random walks Recurrence and Polya number of general one-dimensional random walks

2010-10-11

arxiv.org/abs/1010.2014v1

Commun. Theor. Phys. 56, 293-296 (2011)

Physics

Mathematical Physics

3 page short paper

Scientific paper

The recurrence properties of random walks can be characterized by P\'{o}lya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities $l$ and $r$, or remain at the same position with probability $o$ ($l+r+o=1$). We calculate P\'{o}lya number $P$ of this model and find a simple expression for $P$ as, $P=1-\Delta$, where $\Delta$ is the absolute difference of $l$ and $r$ ($\Delta=|l-r|$). We prove this rigorous expression by the method of creative telescoping, and our result suggests that the walk is recurrent if and only if the left-moving probability $l$ equals to the right-moving probability $r$.

Affiliated with

Also associated with

No associations

Rating

Recurrence and Polya number of general one-dimensional random walks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Recurrence and Polya number of general one-dimensional random walks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Recurrence and Polya number of general one-dimensional random walks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-658245