A Limit Theorem for Shifted Schur Measures
نویسندگان
چکیده
To each partition λ = (λ1, λ2, . . .) with distinct parts we assign the probability Qλ(x)Pλ(y)/Z where Qλ and Pλ are the SchurQ-functions and Z is a normalization constant. This measure, which we call the shifted Schur measure, is analogous to the much-studied Schur measure. For the specialization of the first m coordinates of x and the first n coordinates of y equal to α (0 < α < 1) and the rest equal to zero, we derive a limit law for λ1 as m,n → ∞ with τ = m/n fixed. For the Schur measure the α-specialization limit law was derived by Johansson. Our main result implies that the two limit laws are identical.
منابع مشابه
A Scaling Limit for t-Schur Measures
To each partition λ, we introduce a measure Sλ(x; t)sλ(y)/Zt where sλ is the Schur function and Sλ(x; t) is a generalization of the Schur function defined in [M] and Zt is a normalization constant. This measure, which we call the t-Schur measure, is a generalization of the Schur measure [O] and the shifted Schur measure studied by Tracy and Widom [TW3]. We prove that by a certain specialization...
متن کاملShifted Schur Process and Asymptotics of Large Random Strict Plane Partitions
In this paper we define the shifted Schur process as a measure on sequences of strict partitions. This process is a generalization of the shifted Schur measure introduced in [TW] and [Mat] and is a shifted version of the Schur process introduced in [OR1]. We prove that the shifted Schur process defines a Pfaffian point process. We further apply this fact to compute the bulk scaling limit of the...
متن کاملCorrelation functions of the shifted Schur measure
The shifted Schur measure introduced in [TW2] is a measure on the set of all strict partitions λ = (λ1 > λ2 > · · · > λl > 0), which is defined by Schur Q-functions. The main aim of this paper is to calculate the correlation function of this measure, which is given by a pfaffian. As an application, we prove that a limit distribution of λj ’s with respect to a shifted version of the Plancherel m...
متن کاملRAPPORT Central limit theorem for a class of random measures associated with germ - grain models
The paper introduces a family of stationary random measures in R d generated by so-called germ-grain models. The germ-grain model is deened as the union of i.i.d. compact random sets (grains) shifted by points (germs) of a point process. This model gives rise to random measures deened by the sum of contributions of non-overlapping parts of the individual grains. The corresponding moment measure...
متن کاملar X iv : 0 80 7 . 24 73 v 1 [ m at h . C O ] 1 5 Ju l 2 00 8 DIFFERENTIAL OPERATORS , SHIFTED PARTS , AND HOOK LENGTHS
Pλ(y; θ), (1) where δ := (n− 1, n− 2, . . . , 1, 0) and λ are partitions, aδ = ∏ 1≤i<j≤n(yi − yj) is the Vandermonde determinant and u is a free parameter. Under a general result, S. Sahi proves [8, Theorem 5.2] the existence of a unique polynomial P ∗ μ(y; θ), now known as shifted Jack polynomials, satisfying a certain vanishing condition. In the special case θ = 1, Okounkov and Olshanski [6,7...
متن کامل