The strong interaction limit of continuous-time weakly self-avoiding walk

Details The strong interaction limit of continuous-time weakly self-avoiding walk The strong interaction limit of continuous-time weakly self-avoiding walk

2011-04-19

arxiv.org/abs/1104.3731v1

Mathematics

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Scientific paper

The strong interaction limit of the discrete-time weakly self-avoiding walk (or Domb--Joyce model) is trivially seen to be the usual strictly self-avoiding walk. For the continuous-time weakly self-avoiding walk, the situation is more delicate, and is clarified in this paper. The strong interaction limit in the continuous-time setting depends on how the fugacity is scaled, and in one extreme leads to the strictly self-avoiding walk, in another to simple random walk. These two extremes are interpolated by a new model of a self-repelling walk that we call the "quick step" model. We study the limit both for walks taking a fixed number of steps, and for the two-point function.

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