Random walk weakly attracted to a wall
Probability
2009-11-13 v2 Mathematical Physics
math.MP
Abstract
We consider a random walk X_n in Z_+, starting at X_0=x>= 0, with transition probabilities P(X_{n+1}=X_n+1|X_n=y>=1)=1/2-\delta/(4y+2\delta) P(X_{n+1}=X_n+1|X_n=y>=1)=1/2+\delta/(4y+2\delta) and X_{n+1}=1 whenever X_n=0. We prove that the expectation value of X_n behaves like n^{1-(\delta/2)} as n goes to infinity when \delta is in the range (1,2). The proof is based upon the Karlin-McGregor spectral representation, which is made explicit for this random walk.
Cite
@article{arxiv.0805.0729,
title = {Random walk weakly attracted to a wall},
author = {Joël De Coninck and François Dunlop and Thierry Huillet},
journal= {arXiv preprint arXiv:0805.0729},
year = {2009}
}
Comments
Replacement with minor changes and additions in bibliography. Same abstract, in plain text rather than TeX