论文标题
$φ^4_2 $和$φ^4_3 $测量的log-sobolev不平等
Log-Sobolev inequality for the $φ^4_2$ and $φ^4_3$ measures
论文作者
论文摘要
在晶格正则化中，在最佳假设中，continum $φ^4_2 $和$φ^4_3 $测量表明在晶格正则化中均匀地满足了log-sobolev的不平等。特别是，这适用于所有有限量的所有耦合常数，并且在$φ^4_2 $和$φ^4_3 $型号的整个高温阶段的体积中均匀。 该证明使用Polchinski（肾小效应组）方程式使用了Log-Sobolev不平等的一般标准，最近证明，具有一般外部领域的Ising模型，Perron-Frobenius Theorem，以及使用$φ^4_2 $ $ $ $ qum usefor的usements bongron-frobenius Theorem和界限，这是一种显着的相关性不平等。
The continuum $φ^4_2$ and $φ^4_3$ measures are shown to satisfy a log-Sobolev inequality uniformly in the lattice regularisation under the optimal assumption that their susceptibility is bounded. In particular, this applies to all coupling constants in any finite volume, and uniformly in the volume in the entire high temperature phases of the $φ^4_2$ and $φ^4_3$ models. The proof uses a general criterion for the log-Sobolev inequality in terms of the Polchinski (renormalisation group) equation, a recently proved remarkable correlation inequality for Ising models with general external fields, the Perron--Frobenius theorem, and bounds on the susceptibilities of the $φ^4_2$ and $φ^4_3$ measures obtained using skeleton inequalities.
