Revision as of 03:35, 9 June 2024 by Bot (Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Show that, for an ergodic Markov chain (see Theorem), <math display="block"> \sum_j m_{ij} w_j = \sum_j z_{jj} - 1 = K\ . </math> The second expression above shows that the number <math>K</math> is independent of...")
BBy Bot
Jun 09'24
Exercise
[math]
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Show that, for an ergodic Markov chain (see Theorem),
[[math]]
\sum_j m_{ij} w_j = \sum_j z_{jj} - 1 = K\ .
[[/math]]
The second expression above shows that the number [math]K[/math] is independent of [math]i[/math]. The number [math]K[/math] is called Kemeny's constant. A prize was offered to the first person to give an intuitively plausible reason for the above sum to be independent of [math]i[/math]. (See also Exercise \ref{exer 11.5.27}.)