### Abstract

We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent with analogous mechanical models. Our main result is that the rate of convergence to equilibrium for such a system is ∼t^{-2}, more precisely it is faster than a constant times t^{-2+ε} for any ε > 0. A discussion of exponential vs. polynomial convergence for similar particle systems is included.

Original language | English (US) |
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Pages (from-to) | 65-90 |

Number of pages | 26 |

Journal | Annals of Applied Probability |

Volume | 27 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 2017 |

### Fingerprint

### Keywords

- Interacting particle model
- Markov jump process
- Polynomial convergence rate

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**Polynomial convergence to equilibrium for a system of interacting particles.** / Li, Yao; Young, Lai-Sang.

Research output: Contribution to journal › Article

*Annals of Applied Probability*, vol. 27, no. 1, pp. 65-90. https://doi.org/10.1214/16-AAP1197

}

TY - JOUR

T1 - Polynomial convergence to equilibrium for a system of interacting particles

AU - Li, Yao

AU - Young, Lai-Sang

PY - 2017/2/1

Y1 - 2017/2/1

N2 - We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent with analogous mechanical models. Our main result is that the rate of convergence to equilibrium for such a system is ∼t-2, more precisely it is faster than a constant times t-2+ε for any ε > 0. A discussion of exponential vs. polynomial convergence for similar particle systems is included.

AB - We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent with analogous mechanical models. Our main result is that the rate of convergence to equilibrium for such a system is ∼t-2, more precisely it is faster than a constant times t-2+ε for any ε > 0. A discussion of exponential vs. polynomial convergence for similar particle systems is included.

KW - Interacting particle model

KW - Markov jump process

KW - Polynomial convergence rate

UR - http://www.scopus.com/inward/record.url?scp=85015885617&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015885617&partnerID=8YFLogxK

U2 - 10.1214/16-AAP1197

DO - 10.1214/16-AAP1197

M3 - Article

AN - SCOPUS:85015885617

VL - 27

SP - 65

EP - 90

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 1

ER -