AI 中文总结
针对周期一维Riesz气体，证明粒子位移方差界为β^{-1}量级，并建立Gibbs极限与有序匹配，通过电通量比较给出关键估计。
AI 中文摘要
对于具有局域对势 $-|x|^a$（$0<a<1$）的中性周期一维Riesz气体，我们证明了粒子位移方差界为 $\beta^{-1}$ 量级，且该界对粒子数一致成立。对数凹性还给出了指数型位移尾部。每个平稳周期热力学极限都是简单的，强度为1，并允许与单位格点进行平稳有序匹配，且具有相同的界。每个极限都满足全直线相互作用的典范Gibbs方程，其中外部势采用普通对称空间主值。该匹配意味着均匀有界的区间数方差，以及在足够低的温度下倒格傅里叶平均的正极限二阶矩。主要估计通过确定性电通量将逆随机Hessian与瞬态长程网络进行比较。
英文摘要
For the neutral periodic one-dimensional Riesz gas with pair potential locally $-|x|^a$, $0<a<1$, we prove a particle-displacement variance bound of order $β^{-1}$, uniformly in the number of particles. Log-concavity also gives exponential displacement tails. Every stationary periodic thermodynamic limit is simple, has intensity one, and admits a stationary ordered matching to the unit lattice with the same bounds. Each limit satisfies the canonical Gibbs equations for the full-line interaction, with an ordinary symmetric spatial principal value for the exterior potential. The matching implies uniformly bounded interval number variance and a positive limiting second moment of the reciprocal-lattice Fourier average at sufficiently low temperature. The main estimate compares the inverse random Hessian, through deterministic electrical flows, to a transient long-range network.
Comments21 pages, 1 figure
