The Annals of Applied Probability

One-dimensional long-range diffusion limited aggregation II: The transient case

Gideon Amir, Omer Angel, and Gady Kozma

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Abstract

We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this paper, we handle the case of transient walks.

Article information

Source
Ann. Appl. Probab., Volume 27, Number 3 (2017), 1886-1922.

Dates
Received: July 2015
Revised: July 2016
First available in Project Euclid: 19 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1500451246

Digital Object Identifier
doi:10.1214/16-AAP1248

Mathematical Reviews number (MathSciNet)
MR3678487

Zentralblatt MATH identifier
1375.60035

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Keywords
Diffusion limited aggregation transient random walk harmonic measure growth process

Citation

Amir, Gideon; Angel, Omer; Kozma, Gady. One-dimensional long-range diffusion limited aggregation II: The transient case. Ann. Appl. Probab. 27 (2017), no. 3, 1886--1922. doi:10.1214/16-AAP1248. https://projecteuclid.org/euclid.aoap/1500451246


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References

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