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Border aggregation model

Thacker, Debleena LU and Volkov, Stanislav LU orcid (2018) In Annals of Applied Probability 28(3). p.1604-1633
Abstract
Start with a graph with a subset of vertices called {\it 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 ξ of particles to be released by this final moment.
We show that this model covers OK Corral model as well as the erosion model, and obtain distributions and bounds for ξ in cases where the graph is star graph, regular tree, and a d−dimensional lattice.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Annals of Applied Probability
volume
28
issue
3
pages
30 pages
publisher
Institute of Mathematical Statistics
external identifiers
  • scopus:85048033887
ISSN
1050-5164
DOI
10.1214/17-AAP1339
language
English
LU publication?
yes
id
22bbaa0a-bc07-4733-8a0e-86ff59a61132
date added to LUP
2017-03-03 14:03:56
date last changed
2021-10-06 03:00:50
@article{22bbaa0a-bc07-4733-8a0e-86ff59a61132,
  abstract     = {Start with a graph with a subset of vertices called {\it 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 ξ of particles to be released by this final moment. <br/>We show that this model covers OK Corral model as well as the erosion model, and obtain distributions and bounds for ξ in cases where the graph is star graph, regular tree, and a d−dimensional lattice.},
  author       = {Thacker, Debleena and Volkov, Stanislav},
  issn         = {1050-5164},
  language     = {eng},
  number       = {3},
  pages        = {1604--1633},
  publisher    = {Institute of Mathematical Statistics},
  series       = {Annals of Applied Probability},
  title        = {Border aggregation model},
  url          = {http://dx.doi.org/10.1214/17-AAP1339},
  doi          = {10.1214/17-AAP1339},
  volume       = {28},
  year         = {2018},
}