BC type z-measures and determinantal point processes

@article{Cuenca2018BCTZ,
  title={BC type z-measures and determinantal point processes},
  author={Cesar Cuenca},
  journal={Advances in Mathematics},
  year={2018}
}
  • Cesar Cuenca
  • Published 24 January 2017
  • Mathematics
  • Advances in Mathematics
View PDF on arXiv
7 Citations
Highly Influential Citations
1
Background Citations
3
Methods Citations
2

7 Citations

Infinite 𝑝-adic random matrices and ergodic decomposition of 𝑝-adic Hua measures
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…
The Elliptic Tail Kernel
We introduce and study a new family of $q$-translation-invariant determinantal point processes on the two-sided $q$-lattice. We prove that these processes are limits of the $q$–$zw$ measures, which…
Random surface growth and Karlin-McGregor polynomials
We consider consistent dynamics for non-intersecting birth and death chains, originating from dualities of stochastic coalescing flows and one dimensional orthogonal polynomials. As corollaries, we…
Elements of the q-Askey Scheme in the Algebra of Symmetric Functions
The classical q-hypergeometric orthogonal polynomials are assembled into a hierarchy called the q-Askey scheme. At the top of the hierarchy, there are two closely related families, the Askey-Wilson…
Markov processes on the duals to infinite-dimensional classical Lie groups
  • Cesar Cuenca
  • Mathematics
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
  • 2018
We construct a four parameter (z, z', a, b) family of Markov dynamics that preserve the z-measures on the boundary of the branching graph for classical Lie groups of type B, C, D. Our guiding…
Skew Howe duality and limit shapes of Young diagrams
We consider the skew Howe duality for the action of certain dual pairs of Lie groups (G1, G2) on the exterior algebra ∧ (C ⊗ C) as a probability measure on Young diagrams by the decomposition into…
Macdonald-Level Extension of Beta Ensembles and Large-N Limit Transition
We introduce and study a family of $(q,t)$-deformed discrete $N$-particle beta ensembles, where $q$ and $t$ are the parameters of Macdonald polynomials. The main result is the existence of a…

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…
Coxeter group actions on Saalsch\"utzian ${}_4F_3(1)$ series and very-well-poised ${}_7F_6(1)$ series
Classical Orthogonal Polynomials of a Discrete Variable
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
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
TLDR
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
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
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…
Random partitions and the gamma kernel
Limits of BC-type orthogonal polynomials as the number of variables goes to infinity
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…
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