## 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) |
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Pages (from-to) | 21-32 |

Number of pages | 12 |

Journal | Alea |

Volume | 20 |

Issue number | 1 |

DOIs | |

State | Published - 2023 |

Externally published | Yes |

## Keywords

- Interacting particle systems
- occupation time
- robotics
- simple exclusion process

## ASJC Scopus subject areas

- Statistics and Probability