The self-avoiding stroll is a mathematical version with very important purposes in statistical mechanics and polymer technology. this article offers a unified account of the rigorous effects for the self-avoiding stroll, targeting its serious behaviour. subject matters mentioned contain: the lace explosion and its software to the self-avoiding stroll in additional than 4 dimensions the place such a lot concerns are actually resolved; an advent to the nonrigorous scaling conception; classical paintings of Hammersley and others; an exposition of Kesten's trend theorem and its effects; a dialogue of the decay of the two-point functionality and its relation to probabilistic renewal idea; and the position of the self-avoiding stroll in actual and chemical purposes.

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