Geodesic Forests in the Last-Passage Percolation

López, Sergio I.; Pimentel, Leandro P. R.

doi:10.48550/arxiv.1510.01552

Cited by 2 publications

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“…The IDLA and Eden models were considered by Berger, Kagan and Procaccia [2], and Antunović and Procaccia [1] respectively. Lopez and Pimentel studied a stationary process created by geodesics in Last Passage Percolation [7], and obtained very precise geometric results. A stationary version of DLA on the lattice was introduced and studied by Procaccia et al [12,13,14,15].…”

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Growth of stationary Hastings–Levitov

2022

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We construct and study a stationary version of the Hastings-Levitov(0) model. We prove that, unlike in the classical HL(0) model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL( 0) is proposed as a potential candidate for a stationary off-lattice variant of Diffusion Limited Aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finiteness of arms and arm size distribution. We show that, under appropriate scaling, arms in SHL(0) converge to the graph of Brownian motion which has fractal dimension 3/2. Moreover we show that trees with n particles reach a height of order n 2/3 , corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.

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confidence: 99%