Border aggregation model
Thacker, Debleena LU and Volkov, Stanislav LU
(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:
https://lup.lub.lu.se/record/22bbaa0a-bc07-4733-8a0e-86ff59a61132
- author
- Thacker, Debleena
LU
and Volkov, Stanislav
LU
- organization
- publishing date
- 2018-06
- 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
- 2025-10-14 13:23:58
@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}},
}