The length of self-avoiding walks on the complete graph

@article{Deng2019TheLO,
  title={The length of self-avoiding walks on the complete graph},
  author={Youjin Deng and Timothy M. Garoni and Jens Grimm and Abrahim Nasrawi and Zongzheng Zhou},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2019}
}
We study the variable-length ensemble of self-avoiding walks on the complete graph. We obtain the leading order asymptotics of the mean and variance of the walk length, as the number of vertices goes to infinity. Central limit theorems for the walk length are also established, in various regimes of fugacity. Particular attention is given to sequences of fugacities that converge to the critical point, and the effect of the rate of convergence of these fugacity sequences on the limiting walk… Expand

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