Summary
We construct a self-avoiding process taking values in the finite Sierpinski gasket, and study its properties. We then study “continuum limit” processes that are suggested by the statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We prove that there are three types of continuum limit processes according to the parameters defining the statistical mechanics of self-avoiding paths:
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(i)
the self-avoiding process we construct in this paper;
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(ii)
a deterministic motion along a “Peano curve” on the finite Sierpinski gasket;
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(iii)
a deterministic motion along a line segment.
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Hattori, K., Hattori, T. Self-avoiding process on the Sierpinski gasket. Probab. Th. Rel. Fields 88, 405–428 (1991). https://doi.org/10.1007/BF01192550
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DOI: https://doi.org/10.1007/BF01192550
Keywords
- Stochastic Process
- Probability Theory
- Line Segment
- Statistical Mechanic
- Mathematical Biology