Monotonicity result for the simple exclusion process on finite connected graphs

Shiba Biswal; Nicolas Lanchier

doi:10.30757/ALEA.v20-02

Monotonicity result for the simple exclusion process on finite connected graphs

Research output: Contribution to journal › Article › peer-review

Abstract

The simple exclusion process studied in this paper consists of a system of K particles moving on the vertex set of a finite undirected connected graph. If there is one, the particle at x chooses one of the deg(x) neighbors of its current location uniformly at random at rate ρ_x > 0, and jumps to that vertex if and only if it is empty. Though this model is a natural mathematical object, it is also motivated by applications in the control of robotic swarms. After expressing the stationary distribution and the limiting occupation times of the process, we study how the total number of particles affects the occupation times ratios at different vertices.

Original language	English (US)
Pages (from-to)	21-32
Number of pages	12
Journal	Alea
Volume	20
Issue number	1
DOIs	https://doi.org/10.30757/ALEA.v20-02
State	Published - 2023
Externally published	Yes

Keywords

Interacting particle systems
occupation time
robotics
simple exclusion process

ASJC Scopus subject areas

Statistics and Probability

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10.30757/ALEA.v20-02

Cite this

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title = "Monotonicity result for the simple exclusion process on finite connected graphs",

abstract = "The simple exclusion process studied in this paper consists of a system of K particles moving on the vertex set of a finite undirected connected graph. If there is one, the particle at x chooses one of the deg(x) neighbors of its current location uniformly at random at rate ρx > 0, and jumps to that vertex if and only if it is empty. Though this model is a natural mathematical object, it is also motivated by applications in the control of robotic swarms. After expressing the stationary distribution and the limiting occupation times of the process, we study how the total number of particles affects the occupation times ratios at different vertices.",

keywords = "Interacting particle systems, occupation time, robotics, simple exclusion process",

author = "Shiba Biswal and Nicolas Lanchier",

note = "Funding Information: Received by the editors April 18th, 2022; accepted November 28th, 2022. 2010 Mathematics Subject Classification. 60K35. Key words and phrases. Interacting particle systems, simple exclusion process, occupation time, robotics. Nicolas Lanchier was partially supported by NSF grant CNS-2000792. Publisher Copyright: {\textcopyright} 2023, Alea (Rio de Janeiro).All Rights Reserved.",

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doi = "10.30757/ALEA.v20-02",

language = "English (US)",

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AU - Lanchier, Nicolas

N1 - Funding Information: Received by the editors April 18th, 2022; accepted November 28th, 2022. 2010 Mathematics Subject Classification. 60K35. Key words and phrases. Interacting particle systems, simple exclusion process, occupation time, robotics. Nicolas Lanchier was partially supported by NSF grant CNS-2000792. Publisher Copyright: © 2023, Alea (Rio de Janeiro).All Rights Reserved.

PY - 2023

Y1 - 2023

N2 - The simple exclusion process studied in this paper consists of a system of K particles moving on the vertex set of a finite undirected connected graph. If there is one, the particle at x chooses one of the deg(x) neighbors of its current location uniformly at random at rate ρx > 0, and jumps to that vertex if and only if it is empty. Though this model is a natural mathematical object, it is also motivated by applications in the control of robotic swarms. After expressing the stationary distribution and the limiting occupation times of the process, we study how the total number of particles affects the occupation times ratios at different vertices.

AB - The simple exclusion process studied in this paper consists of a system of K particles moving on the vertex set of a finite undirected connected graph. If there is one, the particle at x chooses one of the deg(x) neighbors of its current location uniformly at random at rate ρx > 0, and jumps to that vertex if and only if it is empty. Though this model is a natural mathematical object, it is also motivated by applications in the control of robotic swarms. After expressing the stationary distribution and the limiting occupation times of the process, we study how the total number of particles affects the occupation times ratios at different vertices.

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Monotonicity result for the simple exclusion process on finite connected graphs

Abstract

Keywords

ASJC Scopus subject areas

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