Abstract
In this chapter we study the limiting behavior of the total number of cycles and of the number of cycles of fixed length in random permutations of [n] as n → ∞. This class of problems springs from a classical question in probability called the envelope matching problem. You have n letters and n addressed envelopes. If you randomly place one letter in each envelope, what is the asymptotic probability as n → ∞ that no letter is in its correct envelope?
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