7 Citations
Infinite 𝑝-adic random matrices and ergodic decomposition of 𝑝-adic Hua measures
- Mathematics
- 2020
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
- MathematicsInternational Mathematics Research Notices
- 2020
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
- Mathematics
- 2017
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
- MathematicsMoscow Mathematical Journal
- 2020
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
- MathematicsAnnales 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
- Mathematics
- 2021
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
- Mathematics
- 2020
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
- Mathematics
- 1998
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
- Mathematics
- 2010
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
- Mathematics
- 1999
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…