非负次临界势对Gibbs分布的唯一性

IF 1.5 Q2 PHYSICS, MATHEMATICAL Annales de l Institut Henri Poincare D Pub Date : 2021-08-13 DOI:10.1214/22-AIHP1265

Steffen Betsch, G. Last

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引用次数: 8

摘要

我们证明了只要泊松驱动随机连接模型(RCM)不渗透，具有非负对势的Gibbs过程的分布是唯一确定的。我们的证明结合了连续体中的不一致耦合与吉布斯过程和RCM的耦合。从理论和仿真两方面说明了该方法对以往唯一性结果的改进。

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On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential

We prove that the distribution of a Gibbs process with non-negative pair potential is uniquely determined as soon as an associated Poisson-driven random connection model (RCM) does not percolate. Our proof combines disagreement coupling in continuum with a coupling of a Gibbs process and a RCM. The improvement over previous uniqueness results is illustrated both in theory and simulations.

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