Poisson limit of bumping routes in the Robinson-Schensted correspondence

TL;DR

This paper studies the bumping routes in the Robinson-Schensted-Knuth algorithm applied to random inputs, showing their convergence to a Poisson process after a coordinate transformation.

Contribution

It establishes the Poisson limit of bumping routes in large Plancherel-distributed tableaux, revealing their asymptotic behavior.

Findings

Bumping routes converge to a Poisson process after transformation

Analysis focused on the vicinity of the y-axis

Results apply to large random tableaux

Abstract

We consider the Robinson-Schensted-Knuth algorithm applied to a random input and investigate the shape of the bumping route (in the vicinity of the $y$-axis) when a specified number is inserted into a large Plancherel-distributed tableau. We show that after a projective change of the coordinate system the bumping route converges in distribution to the Poisson process.