ERGODIC UNITARILY INVARIANT MEASURES ON THE SPACE OF INFINITE HERMITIAN MATRICES

@article{Olshanski1996ERGODICUI,
  title={ERGODIC UNITARILY INVARIANT MEASURES ON THE SPACE OF INFINITE HERMITIAN MATRICES},
  author={Grigori Olshanski and Anatolii Moiseevich Vershik},
  journal={arXiv: Representation Theory},
  year={1996}
}
Let $H$ be the space of all Hermitian matrices of infinite order and $U(\infty)$ be the inductive limit of the chain $U(1)\subset U(2)\subset...$ of compact unitary groups. The group $U(\infty)$ operates on the space $H$ by conjugations, and our aim is to classify the ergodic $U(\infty)$-invariant probability measures on $H$ by making use of a general asymptotic approach proposed in Vershik's note \cite{V}. The problem is reduced to studying the limit behavior of orbital integrals of the form… 
Ergodic measures on infinite skew-symmetric matrices over non-Archimedean local fields
  • Yanqi Qiu
  • Mathematics
    Groups, Geometry, and Dynamics
  • 2019
Let $F$ be a non-discrete non-Archimedean locally compact field such that the characteristic $\mathrm{ch}(F)\ne 2$ and let $\mathcal{O}_F$ be the ring of integers in $F$. The main results of this
Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields
Let $F$ be a non-discrete non-Archimedean locally compact field and ${\mathcal{O}}_{F}$ the ring of integers in $F$ . The main results of this paper are the classification of ergodic probability
Law of Large Numbers for infinite random matrices over a finite field
Asymptotic representation theory of general linear groups $$\hbox {GL}(n,F_\mathfrak {q})$$GL(n,Fq) over a finite field leads to studying probability measures $$\rho $$ρ on the group $$\mathbb {U}$$U
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
Finiteness of Ergodic Unitarily Invariant Measures on Spaces of Infinite Matrices
The main result of this note, Theorem 2, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant under the action of the infinite unitary group and that
Universal Behavior of the Corners of Orbital Beta Processes
  • Cesar Cuenca
  • Mathematics
    International Mathematics Research Notices
  • 2019
There is a unique unitarily-invariant ensemble of $N\times N$ Hermitian matrices with a fixed set of real eigenvalues $a_1> \dots > a_N$. The joint eigenvalue distribution of the $(N-1)$ top-left
Crystallization of random matrix orbits
Three operations on eigenvalues of real/complex/quaternion (corresponding to $\beta=1,2,4$) matrices, obtained from cutting out principal corners, adding, and multiplying matrices can be extrapolated
Invariant states on the wreath product
Let $\mathfrak{S}_\infty$ be the infinity permutation group and $\Gamma$ be a separable topological group. The wreath product $\Gamma\wr \mathfrak{S}_\infty$ is the semidirect product
A new approach to the characteristic polynomial of a random unitary matrix
Since the seminal work of Keating and Snaith, the characteristic polynomial of a random Haar-distributed unitary matrix has seen several of its functional studied or turned into a conjecture; for
Gaussian fluctuations for products of random matrices
abstract:We study global fluctuations for singular values of $M$-fold products of several right-unitarily invariant $N\times N$ random matrix ensembles. As $N\to\infty$, we show the fluctuations of
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 67 REFERENCES
On the Generating Functions of Totally Positive Sequences.
A real matrix, finite or infinite, is called totally positive if and only if all its minors, of all orders = 1, 2,..., are non-negative. An infinite sequence $$ {a_0},{a_1},{a_2}, \ldots ,\quad
Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
1 Introduction to Locally Convex Topological Vector Spaces and Dual Pairs.- 1. Locally Convex Vector Spaces.- 2. Hahn-Banach Theorems.- 3. Dual Pairs.- Notes and Remarks.- 2 Radon Measures and
Irreducible unitary representations of the groups U(p,q) sustaining passage to the limit aS q → ∞
The results of the note are inspired by the theory of representations of the infinite-dimensional classical groups. A new series of irreducible unitary representations of the group U(p,q) is
Heat Kernels and Dirac Operators
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent
Lectures on Choquet's Theorem
Preface.- Introduction. The Krein-Milman theorem as an integral representation theorem.- Application of the Krein-Milman theorem to completely monotonic functions.- Choquet's theorem: The metrizable
The characters of the infinite symmetric group and probability properties of the Robinson-Schensted-Knuth algorithm
Connections between the Robinson–Schensted–Knuth algorithm, random infinite Young tableaux, and central indecomposable measures are investigated. A generalization of the RSK algorithm leads to a
Harmonic analysis on the infinite symmetric group. A deformation of the regular representation
Nous etudions une famille {T z :∈C} de representations unitaires du groupe symetrique denombrable S. C'est une deformation de la representation reguliere T∞. Les principaux resultats sont le calcul
...
1
2
3
4
5
...