为什么Kemeny常数是常数？
Why is Kemeny's constant a constant?
摘要：
在他们1960年的书有限马尔可夫链，凯梅尼和斯内尔建立了一定的总和是不变的。这个和的值被称为{ \it Kemeny常数}。随着时间的推移，已经给出了各种证明，有些比其他人更具技术性。我们在这里给出一个非常简单的物理证明，它顺利地扩展到有限状态空间上的连续时间马尔可夫链。对于状态空间为无穷大的马尔可夫链，常数可能是无穷大的，即使它是有限的，也不能保证物理参数成立。我们表明，物理解释没有通过一个特殊的情况下，生灭过程与有限值的凯梅尼常数。关键词：凯梅尼常数;离散时间马尔可夫链;连续时间马尔可夫链;通过时间;偏差矩阵。
英文摘要：
In their 1960 book on finite Markov chains, Kemeny and Snell established that a certain sum is invariant. The value of this sum has become known as {\it Kemeny's constant}. Various proofs have been given over time, some more technical than others. We give here a very simple physical justification, which extends without a hitch to continuous-time Markov chains on a finite state space. For Markov chains with denumerably infinite state space, the constant may be infinite and even if it is finite, there is no guarantee that the physical argument will hold. We show that the physical interpretation does go through for the special case of a birth-and-death process with a finite value of Kemeny's constant. Keywords: Kemeny's constant; discrete-time Markov chains; continuous-time Markov chains; passage times; deviation matrix.
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