Poisson limit theorems for the Robinson-Schensted correspondence and for the multi-line Hammersley process

Abstract

We consider Robinson-Schensted-Knuth algorithm applied to a random input and study the growth of the bottom rows of the corresponding Young diagrams. We prove multidimensional Poisson limit theorem for the resulting Plancherel growth process. In this way we extend the result of Aldous and Diaconis to more than just one row. This result can be interpreted as convergence of the multi-line Hammersley process to its stationary distribution which is given by a collection of independent Poisson point processes.

version 3. 42 pages. Final version. New: Section 2.7 (conjecture about the rate of convergence)

References in corpus (5)

• Hammersley's process with sources and sinks
• Joint distribution of Busemann functions in the exactly solvable corner growth model
• Representations of Lie groups and random matrices
• Random strict partitions and random shifted tableaux
• Poisson limit of bumping routes in the Robinson-Schensted correspondence

Cited by in corpus (1)

• Poisson limit of bumping routes in the Robinson-Schensted correspondence