Random growth of Young diagrams with uniform marginals
演讲者
Yuri Yakubovich
时间
2023年01月27日 17:00 至 18:30
地点
A6-101
摘要
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.