Random walk weakly attracted to a wall

Details Random walk weakly attracted to a wall Random walk weakly attracted to a wall

2008-05-06

arxiv.org/abs/0805.0729v2

Mathematics

Probability

Replacement with minor changes and additions in bibliography. Same abstract, in plain text rather than TeX

Scientific paper

10.1007/s10955-008-9609-9

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.

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