A Class of Weakly Self-Avoiding Walks |
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| Authors: | Peter Mörters Nadia Sidorova |
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| Institution: | (1) Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK;(2) Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK |
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| Abstract: | We define a class of weakly self-avoiding walks on the integers by conditioning a simple random walk of length n to have a p-fold self-intersection local time smaller than n
β
, where 1<β<(p+1)/2. We show that the conditioned paths grow of order n
α
, where α=(p−β)/(p−1), and also prove a coarse large deviation principle for the order of growth. |
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| Keywords: | Random walk Polymer measure Self-intersection local time Large deviation Law of large numbers |
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