J. Aust. Math. Soc.
75 (2003), 325-353
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Uniform asymptotic estimates of transition probabilities on combs
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Daniela Bertacchi
Università di Milano-Bicocca
Dipartimento di Matematica e Applicazioni
Via Bicocca degli Arcimboldi 8
20126 Milano
Italy
bertacchi@matapp.unimib.it
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Fabio Zucca
Politecnico di Milano
Dipartimento di Matematica
Piazza Leonardo da Vinci 32
20133 Milano
Italy
zucca@mate.polimi.it
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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.
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