论文标题
Liggett定理的新证据
A new proof of Liggett's theorem for non-interacting Brownian motions
论文作者
论文摘要
在本说明中，在特定的独立漂移布朗尼运动的特定情况下，我们给出了有关利格特定理的新证明。由于其应用于分析当地的离散高斯自由领域的极端，最近受到了很多关注。我们证明的新颖性是，它直接识别了预期的泊松点过程，而无需依赖Choquet-deny卷积方程$μ* p =μ$（[Choquetdeny60，denyy60]）。
In this note, we give a new proof of Liggett's theorem on the invariant measures of independent particle systems from [Lig78] in the particular case of independent drifted Brownian motions. This particular case has received a lot of attention recently due to its applications for the analysis of the local extrema of discrete Gaussian free field. The novelty of our proof is that it identifies directly the expected Poisson Point Process with exponential intensity without relying on the Choquet-Deny convolution equation $μ* P=μ$ ([ChoquetDeny60,Deny60]).
