Limiting measures arising in asymptotic theory of symmetric groups

Series: Mathematical Physics and Probability Seminar
Location: Math 402
Presenter: Ibrahim Fatkullin, University of Arizona

I will talk about results of Vershik and Shmidt (1977) regarding the limiting behavior of the Haar (uniform) measure on symmetric groups as their order tends to infinity. In particular, their result implies that the limiting measure can be thought of as a push-forward of the Lebesgue measure on the infinite-dimensional cube onto an infinite dimensional simplex via a simple explicit map.