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2019 Infinite particle systems of long range jumps with long range interactions
Syota Esaki
Tohoku Math. J. (2) 71(1): 9-33 (2019). DOI: 10.2748/tmj/1552100440

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.

Citation

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Syota Esaki. "Infinite particle systems of long range jumps with long range interactions." Tohoku Math. J. (2) 71 (1) 9 - 33, 2019. https://doi.org/10.2748/tmj/1552100440

Information

Published: 2019
First available in Project Euclid: 9 March 2019

zbMATH: 07060324
MathSciNet: MR3920788
Digital Object Identifier: 10.2748/tmj/1552100440

Subjects:
Primary: 60K35
Secondary: 60J75

Rights: Copyright © 2019 Tohoku University

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Vol.71 • No. 1 • 2019
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