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...

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...

Abstract We provide a Plancherel decomposition for the space of symplectic bilinear forms rank $2n$ over local non-Archimedean field $F$ in terms that $\operatorname{GL}_n(F)$.

In the present paper we construct and solve a differential model for the q-analog of the Plancherel growth process. The construction is based on a deformation of the Makrov-Krein correspondence between continual diagrams and probability distributions.

[2] Apparently Fourier did not possess the inner-product expression for (concrete) Fourier coefficients when he first proposed that functions are expressible in Fourier series. This understandably weakened his claim. Worse, at the time, notions of convergence and even the notion of function were amorphous, so that the sense(s) in which a function might be represented by a Fourier series could n...

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...

in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...