Growth by Random Walker Sampling, and Scaling of the Dielectric Breakdown Model

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dc.creatorSomfai, Ellak
dc.creatorGoold, Nicholas R.
dc.creatorBall, Robin C.
dc.creatorDeVita, Jason P.
dc.creatorSander, Leonard M.
dc.date2004-01-21
dc.date.accessioned2026-07-07T02:56:01Z
dc.date.available2026-07-07T02:56:01Z
dc.descriptionRandom walkers absorbing on a boundary sample the Harmonic Measure linearly and independently: we discuss how the recurrence times between impacts enable non-linear moments of the measure to be estimated. From this we derive a new technique to simulate Dielectric Breakdown Model growth which is governed nonlinearly by the Harmonic Measure. Recurrence times are shown to be accurate and effective in probing the multifractal growth measure of diffusion limited aggregation. For the Dielectric Breakdown Model our new technique grows large clusters efficiently and we are led to significantly revise earlier exponent estimates. Previous results by two conformal mapping techniques were less converged than expected, and in particular a recent theoretical suggestion of superuniversality is firmly refuted.
dc.description9 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0401384
dc.identifierhttp://arxiv.org/abs/cond-mat/0401384
dc.identifierPhys. Rev. E 70, 051403 (2004)
dc.identifierdoi:10.1103/PhysRevE.70.051403
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/23157
dc.subjectStatistical Mechanics
dc.titleGrowth by Random Walker Sampling, and Scaling of the Dielectric Breakdown Model
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