 02231 David C. Brydges and John Z. Imbrie
 Green's Function for a Hierarchical SelfAvoiding Walk in Four Dimensions
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May 21, 02

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Abstract. This is the second of two papers on the endtoend distance of a weakly selfrepelling walk on a four dimensional hierarchical lattice. It completes the proof that the expected value grows as a constant times \sqrt{T} log^{1/8}T (1+O((log log T)/log T)), which is the same law as has been conjectured for selfavoiding walks on the simple cubic lattice Z^4.
Apart from completing the program in the first paper, the main result is that the Green's function is almost equal to the Green's function for the Markov process with no selfrepulsion, but at a different value of the killing rate \beta which can be accurately calculated when the interaction is small. Furthermore, the Green's function is analytic in \beta in a sector in the complex plane with opening angle greater than \pi.
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