Internal DLA and the Gaussian free field

Abstract

In previous works, we showed that the internal DLA cluster on \Z^d with t particles is a.s. spherical up to a maximal error of O(\log t) if d=2 and O(\sqrt{\log t}) if d > 2. This paper addresses "average error": in a certain sense, the average deviation of internal DLA from its mean shape is of constant order when d=2 and of order r^{1-d/2} (for a radius r cluster) in general. Appropriately normalized, the fluctuations (taken over time and space) scale to a variant of the Gaussian free field.

29 pages, minor revision

References in corpus (3)

• Lattice points in large regions and related arithmetic functions: Recent developments in a very classic topic
• Sublogarithmic fluctuations for internal DLA
• From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models

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