# BC type z-measures and determinantal point processes

@article{Cuenca2018BCTZ,
title={BC type z-measures and determinantal point processes},
author={Cesar Cuenca},
year={2018}
}
• Cesar Cuenca
• Published 24 January 2017
• Mathematics
Neretin constructed an analogue of the Hua measures on the infinite $p$-adic matrices $Mat\left(\mathbb{N},\mathbb{Q}_p\right)$. Bufetov and Qiu classified the ergodic measures on
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## References

SHOWING 1-10 OF 35 REFERENCES
Point processes and the infinite symmetric group. Part V: Analysis of the matrix Whittaker kernel
The matrix Whittaker kernel has been introduced by A. Borodin in Part IV of the present series of papers. This kernel describes a point process -- a probability measure on a space of countable point
Classical Orthogonal Polynomials of a Discrete Variable
• Mathematics
• 1991
The basic properties of the polynomials p n (x) that satisfy the orthogonality relations $$\int_a^b {{p_n}(x)} {p_m}(x)\rho (x)dx = 0\quad (m \ne n)$$ (2.0.1) hold also for the polynomials
Distributions on Partitions, Point Processes,¶ and the Hypergeometric Kernel
• Mathematics
• 1999
Abstract:We study a 3-parametric family of stochastic point processes on the one-dimensional lattice originated from a remarkable family of representations of the infinite symmetric group. We prove
Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
• Mathematics, Computer Science
• 2001
The first result is that the correlation functions of the Schur process are determinants with a kernel that has a nice contour integral representation in terms of the parameters of the process.
Harmonic analysis on the infinite symmetric group
• Mathematics
• 2003
AbstractThe infinite symmetric group S(∞), whose elements are finite permutations of {1,2,3,...}, is a model example of a “big” group. By virtue of an old result of Murray–von Neumann, the one–sided
Infinite wedge and random partitions
Abstract. We use representation theory to obtain a number of exact results for random partitions. In particular, we prove a simple determinantal formula for correlation functions of what we call the
Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes
• Mathematics
• 2001
The infinite-dimensional unitary group U(∞) is the inductive limit of growing compact unitary groups U(N). In this paper we solve a problem of harmonic analysis on U(∞) stated in [Ol3]. The problem
Limits of BC-type orthogonal polynomials as the number of variables goes to infinity
• Mathematics
• 2006
We describe the asymptotic behavior of the multivariate BC-type Ja- cobi polynomials as the number of variables and the Young diagram indexing the polynomial go to infinity. In particular, our