The self-avoiding walk in a strip

Details The self-avoiding walk in a strip The self-avoiding walk in a strip

2010-08-25

arxiv.org/abs/1008.4321v2

Mathematics

Probability

30 pages, 3 figures

Scientific paper

We review the existence of the infinite length self-avoiding walk in the half plane and its relationship to bridges. We prove that this probability measure is also given by the limit as $\beta \rightarrow \beta_c-$ of the probability measure on all finite length walks $\omega$ with the probability of $\omega$ proportional to $\beta_c^{|\omega|}$ where $|\omega|$ is the number of steps in $\omega$. The self-avoiding walk in a strip $\{z : 0<\Im(z)

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