## 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…

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…

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…

## 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…