\(z\)-measures on partitions, Robinson-Schensted-Knuth correspondence, and \(\beta=2\) random matrix ensembles. (English) Zbl 0987.15013
Bleher, Pavel (ed.) et al., Random matrix models and their applications. Based on talks and lectures from the workshop, Berkeley, CA, USA, February 22-26, 1999. Cambridge: Cambridge University Press. Math. Sci. Res. Inst. Publ. 40, 71-94 (2001).
Summary: We suggest a hierarchy of all the results known so far about the connection of the asymptotics of combinatorial or representation theoretic problems with “\(\beta=2\) ensembles” arising in the random matrix theory. We show that all such results are, essentially, degenerations of one general situation arising from so-called generalized regular representations of the infinite symmetric group.
For the entire collection see [Zbl 0967.00059].
For the entire collection see [Zbl 0967.00059].
MSC:
| 15B52 | Random matrices (algebraic aspects) |
| 05A16 | Asymptotic enumeration |
| 20C32 | Representations of infinite symmetric groups |
