Asymptotics of Plancherel-type random partitions
نویسندگان
چکیده
منابع مشابه
Asymptotics 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 کامل2 0 Fe b 20 07 ASYMPTOTICS 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 کاملCentral Limit Theorem for Random Partitions under the Plancherel Measure
A partition of a natural number n is any integer sequence λ = (λ1, λ2, . . . ) such that λ1 ≥ λ2 ≥ · · · ≥ 0 and λ1 + λ2 + · · · = n (notation: λ ⊢ n). In particular, λ1 = max{λi ∈ λ}. Every partition λ ⊢ n can be represented geometrically by a planar shape called the Young diagram, consisting of n unit cell arranged in consecutive columns, containing λ1, λ2, . . . cells, respectively. On the s...
متن کاملRandom Set Partitions: Asymptotics of Subset Counts
We study the asymptotics of subset counts for the uniformly random partition of the set [n]. It is known that typically most of the subsets of the random partition are of size r, with re=n. Confirming a conjecture formulated by Arratia and Tavare , we prove that the counts of other subsets are close, in terms of the total variation distance, to the corresponding segments of a sequence [Zj] of i...
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 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 Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.10.039