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}
}
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