排斥灵敏度的单调性
Monotonicity properties of exclusion sensitivity
摘要：
在\cite{bgs2013}中，图上对称排它过程的排它敏感性和排它稳定性被定义为噪声敏感性和噪声稳定性的自然类比.由于这些概念是为任意序列的连通图定义的，因此研究这些定义在向图添加边方面的单调性是很自然的，特别是，某些图是否比其他图更稳定或更敏感。本文的主要目的就是回答~ \cite{bgs2013}提出的一些问题。主要工具是完全图上对称排它过程生成元的特征向量和特征值。
英文摘要：
In~\cite{bgs2013}, exclusion sensitivity and exclusion stability for symmetric exclusion processes on graphs were defined as a natural analogue of noise sensitivity and noise stability in this setting. As these concepts were defined for any sequence of connected graphs, it is natural to study the monotonicity properties of these definitions with respect to adding edges to the graphs, and in particular, whether some graphs are more stable or sensitive than others. The main purpose of this paper is to answer some such question from~\cite{bgs2013}. The main tool used is included results about the eigenvectors and eigenvalues of the generator of symmetric exclusion processes on complete graphs.
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