Interval exchange permutations

Anton Zorich
IMJ-PRG, Paris

Date(s) : 30/09/2022   iCal
11 h 00 min - 12 h 00 min


Twenty years ago Vladimir Arnold posed a question on asymptotic statistics of cycle decomposition of special permutations of large number of elements; such permutations can be seen as random integral exchange transformations with a fixed permutation. It was proved by I. Pak and A. Redlich in 2008 that a random interval exchange permutation (A,B,C) -> (C,B,A) is transitive with asymptotic probability $6/pi^2$. However, there was no further progress in Arnold’s problem ever since.

I will present a solution of Arnold’s problem for an arbitrary permutation based, as usual, on combination of combinatorics, geometry, and dynamics of the moduli space of Abelian differentials. En route I will suggest some further conjectures. I will try to make the talk accessible to a general audience. The talk would be in English or in French depending on preferences of the audience.

(joint work with V. Delecroix, E. Goujard, and P. Zograf)


FRUMAM, St Charles (2ème étage)


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