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Selfavoiding walk is subballistic 

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Submitted to  Communications in Mathematical Physics. 2012  
Abstract  We prove that selfavoiding walk on Z^d is subballistic 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 selfavoiding 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}.  
Identifiers  arXiv: 1205.0401  
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Citation (ISO format)  DUMINILCOPIN, Hugo, HAMMOND, Alan. Selfavoiding walk is subballistic. Submitted to: Communications in Mathematical Physics, 2012. https://archiveouverte.unige.ch/unige:30548 