2004/12/14 by Michel Bauer, Bauer, Michel, Denis Bernard +1
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paper · pdf · doi:10.48550/arxiv.cond-mat/0412372
46 pages, 21 figures
arxiv created 2004/12/14 · openalex publication_date 2004/12/14 · arxiv updated 2009/12/01 · openalex created_date 2023/03/07 · openalex updated_date 2026/07/28
These lecture notes on 2D growth processes are divided in two parts. The first part is a non-technical introduction to stochastic Loewner evolutions (SLEs). Their relationship with 2D critical interfaces is illustrated using numerical simulations. Schramm's argument mapping conformally invariant interfaces to SLEs is explained. The second part is a more detailed introduction to the mathematically challenging problems of 2D growth processes such as Laplacian growth, diffusion limited aggregation (DLA), etc. Their description in terms of dynamical conformal maps, with discrete or continuous time evolution, is recalled. We end with a conjecture based on possible dendritic anomalies which, if true, would imply that the Hele-Shaw problem and DLA are in different universality classes.