### Cycle Structure of Random Permutations without long cycles

Probability Seminar

28th February 2020, 3:30 pm – 4:30 pm

Fry Building, 2.41

We analyse the cycle structure of permutations conditioned to have no cycles of volume order. Using methods of

analytic combinatorics, we obtain precise statements about the distribution of cycles, including a limit shape theorem

and Brownian Bridge fluctuations for cumulative cycle numbers. This is joint work with Helge Schäfer (Darmstadt) and Dirk Zeindler (Lancaster).

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