Polynomial convergence to equilibrium for a system of interacting particles. (English) Zbl 1362.60087

Li, Yao; Young, Lai-Sang

Ann. Appl. Probab. 27, No. 1, 65-90 (2017).

Summary: 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 \(\sim t^{-2}\), more precisely it is faster than a constant times \(t^{-2+\varepsilon}\) for any \(\varepsilon>0\). A discussion of exponential vs. polynomial convergence for similar particle systems is included.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60J75	Jump processes (MSC2010)
60J25	Continuous-time Markov processes on general state spaces
60J05	Discrete-time Markov processes on general state spaces
60J20	Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
82C22	Interacting particle systems in time-dependent statistical mechanics

Keywords:

interacting particle model; equilibrium; polynomial convergence rate; Markov jump process