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June 2018 Border aggregation model
Debleena Thacker, Stanislav Volkov
Ann. Appl. Probab. 28(3): 1604-1633 (June 2018). DOI: 10.1214/17-AAP1339


Start with a graph with a subset of vertices called the border. A particle released from the origin performs a random walk on the graph until it comes to the immediate neighbourhood of the border, at which point it joins this subset thus increasing the border by one point. Then a new particle is released from the origin and the process repeats until the origin becomes a part of the border itself. We are interested in the total number $\xi$ of particles to be released by this final moment.

We show that this model covers the OK Corral model as well as the erosion model, and obtain distributions and bounds for $\xi$ in cases where the graph is star graph, regular tree and a $d$-dimensional lattice.


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Debleena Thacker. Stanislav Volkov. "Border aggregation model." Ann. Appl. Probab. 28 (3) 1604 - 1633, June 2018.


Received: 1 February 2017; Revised: 1 July 2017; Published: June 2018
First available in Project Euclid: 1 June 2018

zbMATH: 06919734
MathSciNet: MR3809473
Digital Object Identifier: 10.1214/17-AAP1339

Primary: 60K35 , 82B24

Keywords: Aggregation , DLA model , erosion model , OK Corral model , Random walks

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.28 • No. 3 • June 2018
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