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A Lower Bound on the Disconnection Time of a Discrete Cylinder

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In and Out of Equilibrium 2

Part of the book series: Progress in Probability ((PRPR,volume 60))

Abstract

We study the asymptotic behavior for large N of the disconnection time T N of simple random walk on the discrete cylinder (ℤ/Nℤ)d×ℤ. When d is sufficiently large, we are able to substantially improve the lower bounds on T N previously derived in [3], for d≥2. We show here that the laws of N 2d /T N are tight.

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References

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Author information

Authors and Affiliations

  1. Department of Statistics and Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Amir Dembo

  2. Departement Mathematik, ETH Zürich, CH-8092, Zürich, Switzerland

    Alain-Sol Sznitman

Authors
  1. Amir Dembo
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  2. Alain-Sol Sznitman
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Editor information

Editors and Affiliations

  1. Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina, 110 Jardim Botanico, CEP 22460-320, Rio de Janeiro, RJ, Brasil

    Vladas Sidoravicius

  2. Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150 Urca, 22290-180, Rio de Janeiro, RJ, Brasil

    Maria Eulália Vares

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Dembo, A., Sznitman, AS. (2008). A Lower Bound on the Disconnection Time of a Discrete Cylinder. In: Sidoravicius, V., Vares, M.E. (eds) In and Out of Equilibrium 2. Progress in Probability, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8786-0_10

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