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Self-similarity of harmonic measure on DLA

✍ Scribed by Carl J.G. Evertsz; Benoit B. Mandelbrot

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 513 KB
Volume: 185
Category: Article
ISSN: 0378-4371
DOI: 10.1016/0378-4371(92)90440-2

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✦ Synopsis

The right-hand side of the f(a) curve of the harmonic measure on DLA is undefined. This does not necessarily imply that the harmonic measure and the DLA geometry are not self-similar. We show for off-lattice DLA that the right-hand tail satisfies a different rescaling rule. This Cauchy rescaling is compatible with self-similarity. The analysis is done on off-off-lattice DLA in which both the Brownian motion and the Laplace equation are off-lattice. The cluster sizes range between 32 and 50 000 atoms. The square lattice used to numerically estimate the Laplacian potential introduces a lower cutoff on the spatial resolution of this potential. We find a dependence of the right tail of the distribution of H61ders a on this ultraviolet cutoff. Whereas the shape of the tail does depend on this ultraviolet lattice cutoff, the applicability of the collapse rules do not.

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