Communications in Mathematical Physics

, Volume 97, Issue 1–2, pp 111–124 | Cite as

Intersection properties of simple random walks: A renormalization group approach

  • G. Felder
  • J. Fröhlich
Article

Abstract

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 three random walks ind=3, 3−ε. For ε=0, these results were first obtained by Lawler [1].

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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • G. Felder
    • 1
  • J. Fröhlich
    • 1
  1. 1.Theoretical PhysicsETH-HönggerbergZürichSwitzerland

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