Random walks, diffusion limited aggregation in a wedge, and average conformal maps

Leonard M. Sander; Ellak Somfai

doi:10.1063/1.1876932

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arXiv · cond-mat/0501537

Random walks, diffusion limited aggregation in a wedge, and average conformal maps

Leonard M. Sander·Ellak Somfai

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Abstract

We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that a different, but related, ensemble average, that of the conformal maps associated with random clusters, yields a non-trivial shape which is also not far from the Saffman-Taylor finger. However, we have previously demonstrated that the same average of DLA in a channel geometry is not the Saffman-Taylor finger. This casts doubt on the idea that the average of noisy diffusion-limited growth is governed by a simple transcription of noise-free results.

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Leonard M. Sander, Ellak Somfai. 2005-01-21. Random walks, diffusion limited aggregation in a wedge, and average conformal maps. https://doi.org/10.1063/1.1876932

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