Central Limit Theorem for Random Partitions under the Plancherel Measure
نویسندگان
چکیده
A partition of a natural number n is any integer sequence λ = (λ1, λ2, . . . ) such that λ1 ≥ λ2 ≥ · · · ≥ 0 and λ1 + λ2 + · · · = n (notation: λ ⊢ n). In particular, λ1 = max{λi ∈ λ}. Every partition λ ⊢ n can be represented geometrically by a planar shape called the Young diagram, consisting of n unit cell arranged in consecutive columns, containing λ1, λ2, . . . cells, respectively. On the set Pn := {λ ⊢ n} of all partitions of a given n, consider the Plancherel measure Pn(λ) := dλ n! , λ ∈ Pn, (1)
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