On the Limiting Shape of Young Tableaux Associated With Inhomogeneous Random Words
Christian Houdr\'e, Hua Xu

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.
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Taxonomy
TopicsRandom Matrices and Applications · Advanced Combinatorial Mathematics · Stochastic processes and statistical mechanics
