论文标题
圆形riesz气体的相关性和热力学极限的衰减
Decay of correlations and thermodynamic limit for the circular Riesz gas
论文作者
论文摘要
我们研究了圆形长距离Riesz气体的热力学极限，这是一种通过反功率内核成对相互作用的颗粒系统。我们表明，在重新续订之后，因此典型的颗粒间距为$ 1 $，随着点的数量趋向于无穷大，微观点过程会收敛，而无限体积量$ \ mathrm {riesz} _ {s {s，β} $。通过分析差距相关性获得了这种收敛结果，差距相关性显示在指数$ 2-s $的幂律中衰减。我们的方法基于对Helffer-Sjöstrand方程的分析，其静态形式和各种离散的椭圆规则估计。
We investigate the thermodynamic limit of the circular long-range Riesz gas, a system of particles interacting pairwise through an inverse power kernel. We show that after rescaling, so that the typical spacing of particles is of order $1$, the microscopic point process converges as the number of points tends to infinity, to an infinite volume measure $\mathrm{Riesz}_{s,β}$. This convergence result is obtained by analyzing gaps correlations, which are shown to decay in power-law with exponent $2-s$. Our method is based on the analysis of the Helffer-Sjöstrand equation in its static form and on various discrete elliptic regularity estimates.
