2017年4月
A FAMILY OF SELF-AVOIDING RANDOM WALKS INTERPOLATING THE LOOP-ERASED RANDOM WALK AND A SELF-AVOIDING WALK ON THE SIERPINSKI GASKET
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
- ,
- ,
- 巻
- 10
- 号
- 2
- 開始ページ
- 289
- 終了ページ
- 311
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.3934/dcdss.2017014
- 出版者・発行元
- AMER INST MATHEMATICAL SCIENCES-AIMS
We show that the 'erasing-larger-loops-first' (ELLF) method, which was first introduced for erasing loops from the simple random walk on the Sierpinski gasket, does work also for non-Markov random walks, in particular, self-repelling walks to construct a new family of self-avoiding walks on the Sierpinski gasket. The one-parameter family constructed in this method continuously connects the loop-erased random walk and a self-avoiding walk which has the same asymptotic behavior as the 'standard' self-avoiding walk. We prove the existence of the scaling limit and study some path properties: The exponent nu governing the short-time behavior of the scaling limit varies continuously in the parameter. The limit process is almost surely self-avoiding, while it has path Hausdorff dimension 1/nu, which is strictly greater than 1.
- ID情報
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- DOI : 10.3934/dcdss.2017014