论文标题
检测Ising模型中的结构化信号
Detecting Structured Signals in Ising Models
论文作者
论文摘要
在本文中，我们研究了依赖性在ISING模型中检测一类信号的效果，其中信号以结构化的方式存在。示例包括晶格上的ISING模型，以及平均场类型的ISING模型（Erdős-rényi，随机常规图和密集图）。我们的结果依赖于ISING模型的相关性衰减和混合类型行为，并证明了严格较低信号的关键行为的有益行为。作为我们证明技术的副产品，我们在所有温度方案中的几种平均场类型ISING模型中对混合和自旋旋转相关性进行了敏锐的控制 - 这可能具有独立的兴趣。
In this paper, we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising Models on lattices, and Mean-Field type Ising Models (Erdős-Rényi, Random regular, and dense graphs). Our results rely on correlation decay and mixing type behavior for Ising Models, and demonstrate the beneficial behavior of criticality in the detection of strictly lower signals. As a by-product of our proof technique, we develop sharp control on mixing and spin-spin correlation for several Mean-Field type Ising Models in all regimes of temperature -- which might be of independent interest.
