Tohoku Mathematical Journal

Infinite particle systems of long range jumps with long range interactions

Syota Esaki

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Abstract

In this paper a general theorem for constructing infinite particle systems of jump type with long range interactions is presented. It can be applied to the system that each particle undergoes an $\alpha$-stable process and interaction between particles is given by the logarithmic potential appearing random matrix theory or potentials of Ruelle's class with polynomial decay. It is shown that the system can be constructed for any $\alpha \in (0, 2)$ if its equilibrium measure $\mu$ is translation invariant, and $\alpha$ is restricted by the growth order of the 1-correlation function of the measure $\mu$ in general case.

Article information

Source
Tohoku Math. J. (2), Volume 71, Number 1 (2019), 9-33.

Dates
First available in Project Euclid: 9 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1552100440

Digital Object Identifier
doi:10.2748/tmj/1552100440

Mathematical Reviews number (MathSciNet)
MR3920788

Zentralblatt MATH identifier
07060324

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J75: Jump processes

Keywords
interacting Lévy processes infinitely particle systems Dirichlet form jump type logarithmic potential

Citation

Esaki, Syota. Infinite particle systems of long range jumps with long range interactions. Tohoku Math. J. (2) 71 (2019), no. 1, 9--33. doi:10.2748/tmj/1552100440. https://projecteuclid.org/euclid.tmj/1552100440


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