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Uniform asymptotic estimates of transition probabilities on combs

Published online by Cambridge University Press:  09 April 2009

Daniela Bertacchi
Affiliation:
Università di Milano-BicoccaDipartimento di Matematica e Applicazioni Via Bicocca degli Arcimboldi 8 20126 Milano, Italy e-mail: [email protected]
Fabio Zucca
Affiliation:
Politecnico di Milano, Dipartimento di Matematica, Piazza Leonardo da Vinci 32 20133 Milano, Italy e-mail: [email protected]
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Abstract

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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 sub-Gaussian estimates involving the spectral and walk dimensions of the graph.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

References

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