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Self-avoiding walk is sub-ballistic

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Submitted to Communications in Mathematical Physics. 2012
Abstract We prove that self-avoiding walk on Z^d is sub-ballistic in any dimension d at least two. That is, writing ||u|| for the Euclidean norm of u in Z^d, and SAW_n for the uniform measure on self-avoiding walks gamma:{0,...,n} o Z^d for which gamma_0 = 0, we show that, for each v > 0, there exists c > 0 such that, for each positive integer n, SAW_n (max {|| gamma_k || : k in {0,...,n}} > v n) < e^{- c n}.
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arXiv: 1205.0401
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DUMINIL-COPIN, Hugo, HAMMOND, Alan. Self-avoiding walk is sub-ballistic. Submitted to: Communications in Mathematical Physics, 2012. https://archive-ouverte.unige.ch/unige:30548

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Deposited on : 2013-10-21

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