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June 2021 A Multi-parameter Family of Self-avoiding Walks on the Sierpiński Gasket
Takafumi OTSUKA
Tokyo J. Math. 44(1): 251-283 (June 2021). DOI: 10.3836/tjm/1502179338

Abstract

In this paper, we construct a multi-parameter family of self-avoiding walks on the Sierpiński gasket. It includes the branching model, the loop-erased random walk and the loop-erased self-repelling walk. We reproduce in a unified manner the proof of the existence of the continuum limit and the self-avoiding property of the limit processes. Our limit processes include not only all the processes obtained from the previously studied self-avoiding walk models, but also the ones that have not been constructed before. While the paths of limit processes appearing in the previous works were self-avoiding or filled the whole space, our family includes continuous processes whose path is self-intersecting but does not fill the whole space.

Citation

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Takafumi OTSUKA. "A Multi-parameter Family of Self-avoiding Walks on the Sierpiński Gasket." Tokyo J. Math. 44 (1) 251 - 283, June 2021. https://doi.org/10.3836/tjm/1502179338

Information

Published: June 2021
First available in Project Euclid: 9 July 2021

Digital Object Identifier: 10.3836/tjm/1502179338

Subjects:
Primary: 60F99
Secondary: 28A80, 37F25, 37F35, 60G17

Rights: Copyright © 2021 Publication Committee for the Tokyo Journal of Mathematics

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Vol.44 • No. 1 • June 2021
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