论文标题
一种随机分析方法，用于阳阳的杨 - 在强耦合时磨坊
A stochastic analysis approach to lattice Yang--Mills at strong coupling
论文作者
论文摘要
我们开发了一种新的随机分析方法，以在任何维度$ d> 1 $上以强耦合为lattice yangs模型，t'hooft缩放$βn$用于逆耦合强度。我们研究了他们的Langevin动力学，千古，功能性不平等，大$ n $限制和大规模差距。 假设$ |β| <\ frac {n-2} {32（d-1）n} $用于结构组$ so（n）$或$ |β| <\ frac {1} {16（d-1）} $对于$ su（n）$，我们证明了以下结果。相应的langevin动态的不变度在整个晶格上是唯一的，并且在Wasserstein距离下，动态是指数的。有限体积杨 - 米尔斯测量在无限体积限制中融合了这一独特的不变度度量，对log-sobolev和poincaré的不平等存在。这些功能性不平等意味着，适当重新缩放的无限体积量度的威尔逊循环具有分解的相关性，并收敛于大$ n $限制中的确定性限制，并且大量可观察到的衰减的相关性呈指数性衰减，即无限体积度量的质量严格为正质量质量差异。我们的方法改善了早期的结果或简化了证明，并为Lattice Yangs模型的研究提供了一些新的观点。
We develop a new stochastic analysis approach to the lattice Yang--Mills model at strong coupling in any dimension $d>1$, with t' Hooft scaling $βN$ for the inverse coupling strength. We study their Langevin dynamics, ergodicity, functional inequalities, large $N$ limits, and mass gap. Assuming $|β| < \frac{N-2}{32(d-1)N}$ for the structure group $SO(N)$, or $|β| < \frac{1}{16(d-1)}$ for $SU(N)$, we prove the following results. The invariant measure for the corresponding Langevin dynamic is unique on the entire lattice, and the dynamic is exponentially ergodic under a Wasserstein distance. The finite volume Yang--Mills measures converge to this unique invariant measure in the infinite volume limit, for which Log-Sobolev and Poincaré inequalities hold. These functional inequalities imply that the suitably rescaled Wilson loops for the infinite volume measure has factorized correlations and converges in probability to deterministic limits in the large $N$ limit, and correlations of a large class of observables decay exponentially, namely the infinite volume measure has a strictly positive mass gap. Our method improves earlier results or simplifies the proofs, and provides some new perspectives to the study of lattice Yang--Mills model.
