Limit shapes of bumping routes in the Robinson-Schensted correspondence

8 years 16 days ago

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Abstract. We prove a limit shape theorem describing the asymptotic shape of bumping routes when the Robinson-Schensted algorithm is applied to a ﬁnite sequence of independent, identically distributed random variables with the uniform distribution U[0, 1] on the unit interval, followed by an insertion of a deterministic number α. The bumping route converges after scaling, in the limit as the length of the sequence tends to inﬁnity, to an explicit, deterministic curve depending only on α. This extends our previous result on the asymptotic determinism of Robinson-Schensted insertion, and answers a question posed by Moore in 2006.

Dan Romik, Piotr Sniady

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