# Intersection properties of simple random walks: A renormalization group approach

@article{Felder1985IntersectionPO, title={Intersection properties of simple random walks: A renormalization group approach}, author={Giovanni Felder and Jürg Fröhlich}, journal={Communications in Mathematical Physics}, year={1985}, volume={97}, pages={111-124} }

- Published 1985
DOI:10.1007/bf01206181

We study estimates for the intersection probability,g(m), of two simple random walks on lattices of dimensiond=4, 4−ε as a problem in Euclidean field theory. We rigorously establish a renormalization group flow equation forg(m) and bounds on the β-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−ε is bounded by const' ε≦g*≦constε. Our methods also yield estimates on the intersection probability of… CONTINUE READING

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