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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Mörters, P., Sidorova, N. A Class of Weakly Self-Avoiding Walks. J Stat Phys 133, 255–269 (2008). https://doi.org/10.1007/s10955-008-9619-7
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DOI: https://doi.org/10.1007/s10955-008-9619-7