  Consider the following Markov chain on permutations of length $n$. At each
time step we choose a random position. If the letter at that position is
smaller than the letter immediately to the left (cyclically) then these letters
swap positions. Otherwise nothing happens, corresponding to a loop in the
Markov chain. This is the circular TASEP. We compute the average proportion of
time the chain spends at the identity permutation (and, in greater generality,
at sorted words). This answers a conjecture by Thomas Lam.
