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تسجيل مستخدم جديدGreens Function for a Hierarchical Self-Avoiding Walk in Four Dimensions
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This is the second of two papers on the end-to-end distance of a weakly self-repelling 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 self-avoiding walks on the simple cubic lattice Z^4. - Apart from completing the program in the first paper, the main result is that the Greens function is almost equal to the Greens function for the Markov process with no self-repulsion, but at a different value of the killing rate beta which can be accurately calculated when the interaction is small. Furthermore, the Greens function is analytic in beta in a sector in the complex plane with opening angle greater than pi.
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In [BEI] we introduced a Levy process on a hierarchical lattice which is four dimensional, in the sense that the Greens function for the process equals 1/x^2. If the process is modified so as to be weakly self-repelling, it was shown that at the crit
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