Asymptotics of Plancherel measures for symmetric groups
نویسندگان
چکیده
منابع مشابه
Asymptotics of Plancherel Measures for Symmetric Groups
1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a representation π ∈ G∧ the weight (dim π)/|G|. For the symmetric group S(n), the set S(n)∧ is the set of partitions λ of the number n, which we shall identify with Young diagrams with n squares throughout th...
متن کاملASYMPTOTICS OF q-PLANCHEREL MEASURES
In this paper, we are interested in the asymptotic size of the rows and columns of a random Young diagram under a natural deformation of the Plancherel measure coming from Hecke algebras. The first lines of such diagrams are typically of order n, so it does not fit in the context of the work of P. Biane and P. Śniady. Using the theory of polynomial functions on Young diagrams of Kerov and Olsha...
متن کاملAsymptotics of Plancherel – Type Random Partitions
We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel–type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set Z+ of nonnegative integers. This can be viewed as an edge limit transition. The limit process is determined by a correlation kernel on Z+ which is expressed throug...
متن کاملAsymptotics of Characters of Symmetric Groups and Free Probability
In order to answer the question “what is the asymptotic theory of representations of Sn” we will present two concrete problems. In both cases the solution requires a good understanding of the product (convolution) of conjugacy classes in the symmetric group and we will present a combinatorial setup for explicit calculation of such products. The asymptotic behavior of each summand in our expansi...
متن کاملAsymptotics of Generating the Symmetric and Alternating Groups
The probability that a random pair of elements from the alternating group An generates all of An is shown to have an asymptotic expansion of the form 1¡1/n¡ 1/n2¡4/n3¡23/n4¡171/n5¡ ... . This same asymptotic expansion is valid for the probability that a random pair of elements from the symmetric group Sn generates either An or Sn. Similar results hold for the case of r generators (r > 2). MSC 2...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2000
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-00-00337-4