Intersection properties of simple random walks: A renormalization group approach |
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Authors: | G Felder J Fröhlich |
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Institution: | (1) Theoretical Physics, ETH-Hönggerberg, CH-8093 Zürich, Switzerland |
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Abstract: | We study estimates for the intersection probability,g(m), of two simple random walks on lattices of dimensiond=4, 4– as a problem in Euclidean field theory. We rigorously establish a renormalization group flow equation forg(m) and bounds on the -function which show that, ind=4,g(m) tends to zero logarithmically as the killing rate (mass)m tends to zero, and that the fixed point,g*, ind=4– is bounded by const' ![epsi](/content/k285728674604214/xxlarge949.gif) g* const . Our methods also yield estimates on the intersection probability of three random walks ind=3, 3– . For =0, these results were first obtained by Lawler 1]. |
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