Uniform asymptotic estimates of transition probabilities on combs

Mathematics – Probability

Scientific paper

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31 pages

Scientific paper

We investigate the asymptotical behaviour of the transition probabilities of
the simple random walk on the 2-comb. In particular we obtain space-time
uniform asymptotical estimates which show the lack of symmetry of this walk
better than local limit estimates. Our results also point out the impossibility
of getting Jones-type non-Gaussian estimates.

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