On the Limiting Shape of Young Tableaux Associated With Inhomogeneous Random Words

TL;DR

This paper characterizes the limiting shape of Young diagrams derived from inhomogeneous random words as a multidimensional Brownian functional, linking it to random matrix spectra and analyzing asymptotic behaviors.

Contribution

It introduces a novel connection between the shape of Young diagrams from inhomogeneous words and multidimensional Brownian functionals, extending understanding of their asymptotic properties.

Findings

Limiting shape described by a multidimensional Brownian functional

Equivalence to the spectrum of a random matrix

Asymptotic analysis of the Poissonized word problem

Abstract

The limiting shape of the random Young diagrams associated with an inhomogeneous random word is identified as a multidimensional Brownian functional. This functional is identical in law to the spectrum of a random matrix. The Poissonized word problem is also briefy studied, and the asymptotic behavior of the shape analyzed.