Cutoff Phenomenon for Nearest Lamperti’s Random Walk View Full Text


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Article Info

DATE

2018-08-31

AUTHORS

Wenming Hong, Hui Yang

ABSTRACT

We consider transient neighbor random walks on the positive part of the real line, the transition probability is state dependent being a special case of the Lamperti’s random walk. We show that a sequence of lazy random walks on [0, n] exhibits cutoff phenomenon. As an important step in the proof, we derive the limit speed of the expectation and variance of the hitting times of the random walk exactly. And as a byproduct, we give a probabilistic proof for the law of large numbers of the random walk which has been obtained by Voit (1992) using the method of polynomial hypergroups. More... »

PAGES

1-14

References to SciGraph publications

  • 2009-12. Transient Nearest Neighbor Random Walk and Bessel Process in JOURNAL OF THEORETICAL PROBABILITY
  • 2009-03. Transient Nearest Neighbor Random Walk on the Line in JOURNAL OF THEORETICAL PROBABILITY
  • 2010-01. Total variation cutoff in birth-and-death chains in PROBABILITY THEORY AND RELATED FIELDS
  • 1992-03. Strong laws of large numbers for random walks associated with a class of one-dimensional convolution structures in MONATSHEFTE FÜR MATHEMATIK
  • 1977. Wahrscheinlichkeitstheorie in NONE
  • 2015-06. Mixing Times are Hitting Times of Large Sets in JOURNAL OF THEORETICAL PROBABILITY
  • 2010-06. On the Number of Cutpoints of the Transient Nearest Neighbor Random Walk on the Line in JOURNAL OF THEORETICAL PROBABILITY
  • 1990-12. A law of the iterated logarithm for a class of polynomial hypergroups in MONATSHEFTE FÜR MATHEMATIK
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11009-018-9666-8

    DOI

    http://dx.doi.org/10.1007/s11009-018-9666-8

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1106473664


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