Statistics of Young Diagrams of Cycles of Dynamical Systems for Finite Tori Automorphisms
نویسنده
چکیده
A permutation of a set of N elements is decomposing this set into y cycles of lengths xs, defining a partition N = x1 + · · · + xy. The length X1, the height y and the fullness λ = N/xy of the Young diagram x1 ≥ x2 ≥ · · · ≥ xy behave for the large random permutation like x ∼ an, y ∼ b lnN , λ ∼ c/ lnN . The finite 2-torus M is the product Zm × Zm, and its Fibonacci automorphism sends (u, v) to (2u+v, u+v) (modm). This permutation ofN = m points of the finite torusM defines a peculiar Young diagram, whose behavior (for large m) is very different from that of a random permutation of N points. 2000 Math. Subj. Class. 05E10.
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