The Schelling model on Z
Deijfen, Maria and Vilkas, Timo LU
(2021)
In Annales de l'institut Henri Poincare (B) Probability and Statistics
57(2).
p.800-814
- Abstract
A version of the Schelling model on Z is defined, where two types of agents are allocated on the sites. An agent prefers to be surrounded by other agents of its own type, and may choose to move if this is not the case. It then sends a request to an agent of opposite type chosen according to some given moving distribution and, if the move is beneficial for both agents, they swap location. We show that certain choices in the dynamics are crucial for the properties of the model. In particular, the model exhibits different asymptotic behavior depending on whether the moving distribution has bounded or unbounded support. Furthermore, the behavior changes if the agents are lazy in the sense that they only swap location if this strictly... (More)
A version of the Schelling model on Z is defined, where two types of agents are allocated on the sites. An agent prefers to be surrounded by other agents of its own type, and may choose to move if this is not the case. It then sends a request to an agent of opposite type chosen according to some given moving distribution and, if the move is beneficial for both agents, they swap location. We show that certain choices in the dynamics are crucial for the properties of the model. In particular, the model exhibits different asymptotic behavior depending on whether the moving distribution has bounded or unbounded support. Furthermore, the behavior changes if the agents are lazy in the sense that they only swap location if this strictly improves their situation. Generalizations to a version that includes multiple types are discussed. The work provides a rigorous analysis of so called Kawasaki dynamics on an infinite structure with local interactions.
(Less)
- author
- Deijfen, Maria
and Vilkas, Timo
LU
- publishing date
- 2021-05
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Asymptotic behavior, Interacting particle systems, Kawasaki dynamics, Schelling segregation model, Voter model
- in
- Annales de l'institut Henri Poincare (B) Probability and Statistics
- volume
- 57
- issue
- 2
- pages
- 15 pages
- publisher
- Gauthier-Villars
- external identifiers
-
- scopus:85106365833
- ISSN
- 0246-0203
- DOI
- 10.1214/20-AIHP1096
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2021 Institute of Mathematical Statistics. All rights reserved.
- id
- 03bce42d-81a1-42fd-87bc-2323fb2eebc3
- date added to LUP
- 2023-12-14 13:16:22
- date last changed
- 2023-12-14 15:08:35
@article{03bce42d-81a1-42fd-87bc-2323fb2eebc3,
abstract = {{<p>A version of the Schelling model on Z is defined, where two types of agents are allocated on the sites. An agent prefers to be surrounded by other agents of its own type, and may choose to move if this is not the case. It then sends a request to an agent of opposite type chosen according to some given moving distribution and, if the move is beneficial for both agents, they swap location. We show that certain choices in the dynamics are crucial for the properties of the model. In particular, the model exhibits different asymptotic behavior depending on whether the moving distribution has bounded or unbounded support. Furthermore, the behavior changes if the agents are lazy in the sense that they only swap location if this strictly improves their situation. Generalizations to a version that includes multiple types are discussed. The work provides a rigorous analysis of so called Kawasaki dynamics on an infinite structure with local interactions.</p>}},
author = {{Deijfen, Maria and Vilkas, Timo}},
issn = {{0246-0203}},
keywords = {{Asymptotic behavior; Interacting particle systems; Kawasaki dynamics; Schelling segregation model; Voter model}},
language = {{eng}},
number = {{2}},
pages = {{800--814}},
publisher = {{Gauthier-Villars}},
series = {{Annales de l'institut Henri Poincare (B) Probability and Statistics}},
title = {{The Schelling model on Z}},
url = {{http://dx.doi.org/10.1214/20-AIHP1096}},
doi = {{10.1214/20-AIHP1096}},
volume = {{57}},
year = {{2021}},
}