TITLE: Random permutations of $\mathbb{Z}_n$
QUESTION [5 upvotes]: In "The maximum number of Hamiltonian paths in tournaments" by Noga Alon, the author states the following without proof (equation 3.1):
Consider a random permutation $\pi$ of $\mathbb{Z}_n$. What is the probability that $\pi(i+1)-\pi(i) \pmod{n} <n/2$ for all $i$?
The claim is that this is $(2+o(1))^{-n}$, which makes sense and seems like it should be a standard argument. Does anyone have a formal proof?

REPLY [2 votes]: This question was answered at MathOverflow:
https://mathoverflow.net/questions/54051/random-permutations-of-z-n