Random growth of Young diagrams with uniform marginals

Abstract: Many (random) growth procedures for integer partitions/Young diagrams has been introduced in the literature and intensively studied. The examples include Pitman's `Chinese restaurant' construction, Kerov's Plancherel growth and many others. These procedures amount to insertion of a new box to a Young diagram on each step, following certain Markovian procedure. However, no such procedure leading to the uniform measure on partitions of $n$ after $n$ steps is known. I will describe a Markiovian procedure of adding a rectangular block to a Young diagram with the property that given the growing chain visits some level $n$, it passes through each partition of $n$ with equal probabilities, thus leading to the uniform measure on levels. I will explain connections to some classical probabilistic objects. Also I plan to discuss some aspects of asymptotic behavior of this Markov chain and explain why the limit shape is formed.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( slides | video )

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BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

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