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2017

Stationary Harmonic Measure and DLA in the Upper half Plane

Procaccia, Eviatar B., Zhang, Yuan

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In this paper, we introduce the stationary harmonic measure in the upper half plane.

By bounding this measure, we are able to define both the discrete and continuous time diffusion limit aggregation (DLA) in the upper half plane with absorbing boundary conditions.
We prove that for the continuous model the growth rate is bounded from above by $o(t^{2+\epsilon})$.
When time is discrete, we also prove a better upper bound of $o(n^{2/3+\epsilon})$, on the maximum height of the aggregate at time $n$.

Stationary Harmonic Measure and DLA in the Upper half Plane · Around

Built on

Some problems on random walk in space
A. Dvoretzky and P. Erdös · 1951
Earlier work this paper cites.
Some problems concerning the structure of random walk paths
P. Erdös and S. J. Taylor · 1960
Earlier work this paper cites.
Diffusion-limited aggregation
T. A. Witten and L. M. Sander · 1983
Earlier work this paper cites.
Hitting probabilities of random walks on 𝐙 d {\bf Z}^{d}
H. Kesten · 1987
Earlier work this paper cites.

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