= Stationary position of a transposed distinguished book
{title2=$\pi_i\propto\left(\frac{1-p}{p(N-1)}\right)^{i-1}$}
If a distinguished book is selected with <probability> $p$ and each other book with <probability> $q=(1-p)/(N-1)$, swapping the selected book with its left neighbor makes the distinguished position a <birth-death chain> with left rate $p$ and right rate $q$. Stationary <flow balance> gives successive probabilities in ratio $q/p$, yielding a truncated <geometric distribution>; the uniform case occurs when all books are equally likely.
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