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Logarithmic Fluctuations for Internal DLA
Logarithmic Fluctuations Internal DLA
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2015/8/14
Let each of n particles starting at the origin in Z2 perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resulting random set A(n) ...
Internal DLA in Higher Dimensions
Internal DLA Higher Dimensions
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2015/8/14
Let A(t) denote the cluster produced by internal diffusion limited aggregation (internal DLA) with t particles in dimension d ≥ 3. We show that A(t) is approximately spherical, up to an O(√log t) erro...
Internal DLA and the Gaussian free field
Internal DLA Gaussian free field
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2015/8/14
In previous works, we showed that the internal DLA cluster on Zd with t particles is almost surely spherical up to a maximal error of O(log t) if d = 2 and O(√log t) if d ≥ 3. This paper addresses “av...
Internal DLA in Higher Dimensions
Internal DLA Higher Dimensions
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2011/2/21
Let A(t) denote the cluster produced by internal di usion limited aggregation (internal DLA) with t particles in dimension d 3. We show that A(t) is approximately spherical, up to an O(
p log t) er...
Sub-logarithmic fluctuations for internal DLA
Sub-logarithmic fluctuations internal DLA
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2010/11/23
We consider internal diffusion limited aggregation in dimension larger or equal to two. This is a random cluster growth model, where random walks start at the origin of the $d$-dimensional lattice, o...
From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models
internal diffusion limited aggregation cluster growth
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2010/12/6
We consider a family of cluster growth models on Zd, which generalize internal diffusion limited aggregation (internal DLA). The latter model is simplest to describe:random walks start at the origin, ...