Random Young diagrams in a Rectangular Box
Dan Beltoft (IMF), C\'edric Boutillier (PMA, DMA), Nathana\"el, Enriquez (PMA, MODAL'X)

TL;DR
This paper determines the typical shape of random Young diagrams constrained within a rectangle, showing how their fluctuations relate to Ornstein-Uhlenbeck bridges, thus advancing understanding of their probabilistic geometry.
Contribution
It introduces the limit shape for Young diagrams with exponential area distribution in a rectangle and links fluctuations to Ornstein-Uhlenbeck bridges, a novel probabilistic connection.
Findings
Identified the limit shape of constrained Young diagrams.
Connected fluctuations to Ornstein-Uhlenbeck bridges.
Provided a probabilistic description of the diagrams' geometry.
Abstract
We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Random Matrices and Applications · Advanced Mathematical Identities
