A Class of Weakly Self-Avoiding Walks

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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 nβ, where 1<β<(p+1)/2. We show that the conditioned paths grow of order nα, where α=(p−β)/(p−1), and also prove a coarse large deviation principle for the order of growth.

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