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Time Regularity for Random Walks on Locally Compact Groups
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  • Published: 21 April 2006

Time Regularity for Random Walks on Locally Compact Groups

  • Nick Dungey1 

Probability Theory and Related Fields volume 137, pages 429–442 (2007)Cite this article

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Abstract

Let G be a compactly generated, locally compact group, and let T be the operator of convolution with a probability measure μ on G. Our main results give sufficient conditions on μ for the operator T to be analytic in L p(G), 1 < p < ∞, where analyticity means that one has an estimate of form \(\Vert (I-T)T^n \Vert \leq cn^{-1}\) for all n = 1, 2, ...  in L p operator norm. Counterexamples show that analyticity may not hold if some of the conditions are not satisfied.

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Authors and Affiliations

  1. School of Mathematics, The University of New South Wales, Sydney, 2052, Australia

    Nick Dungey

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  1. Nick Dungey
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Correspondence to Nick Dungey.

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Dungey, N. Time Regularity for Random Walks on Locally Compact Groups. Probab. Theory Relat. Fields 137, 429–442 (2007). https://doi.org/10.1007/s00440-006-0006-5

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  • Received: 15 November 2005

  • Revised: 14 March 2006

  • Published: 21 April 2006

  • Issue Date: March 2007

  • DOI: https://doi.org/10.1007/s00440-006-0006-5

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Keywords

  • Locally compact group
  • Probability measure
  • Convolution operator
  • Random walk

Mathematics Subject Classification (2000)

  • 60B15
  • 60G50
  • 22D05
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