Related papers: Intertwinings for general $\beta$-Laguerre and $\b…
We show that for all positive beta the semigroups of beta-Dyson Brownian motions of different dimensions are intertwined. The proof relates beta-Dyson Brownian motions directly to Jack symmetric polynomials and omits an approximation of the…
We study in some generality intertwinings between $h$-transforms of Karlin-McGregor semigroups associated with one dimensional diffusion processes and those of their Siegmund duals. We obtain couplings so that the corresponding processes…
We introduce multilevel versions of Dyson Brownian motions of arbitrary parameter $\beta>0$, generalizing the interlacing reflected Brownian motions of Warren for $\beta=2$. Such processes unify $\beta$ corners processes and Dyson Brownian…
We study the asymptotics of the global fluctuations for the difference between two adjacent levels in the $\beta$--Jacobi corners process (multilevel and general $\beta$ extension of the classical Jacobi ensemble of random matrices). The…
The aim of this paper is to study intertwining relations for Laguerre process with inverse temperature $\beta \ge 1$ and parameter $\alpha >-1$. We introduce a Markov kernel that depends on both $\beta $ and $ \alpha $, and establish new…
We study Markov chains formed by squared singular values of products of truncated orthogonal, unitary, symplectic matrices (corresponding to the Dyson index $\beta = 1,2,4$ respectively) where time corresponds to the number of terms in the…
We define a new diffusive matrix model converging towards the $\beta$ -Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
Multilevel Dyson Brownian motions (MDBMs) combine Dyson Brownian motions of different dimensions into a single process in a canonical way. This paper completes the theory of MDBMs for $\beta\ge2$. Specifically, we use the superposition…
We show that the Brydges-Fr\"ohlich-Spencer-Dynkin and the Le Jan's isomorphisms between the Gaussian free fields and the occupation times of symmetric Markov processes generalize to the $\beta$-Dyson's Brownian motion. For…
We study $\beta$-Jacobi diffusion processes on alcoves in $\mathbb R^N$, depending on 3 parameters. Using elementary symmetric functions, we present space-time-harmonic functions and martingales for these processes $(X_t)_{t\ge0}$ which are…
We study multilevel matrix ensembles at general beta by identifying them with a class of processes defined via the branching rules for multivariate Bessel and Heckman-Opdam hypergeometric functions. For beta = 1, 2, we express the joint…
We study the global fluctuations for linear statistics of the form $\sum_{i=1}^n f(\lambda_i)$ as $n \rightarrow \infty$, for $C^1$ functions $f$, and $\lambda_1, ..., \lambda_n$ being the eigenvalues of a (general) $\beta$-Jacobi ensemble,…
We study the correlations of the celebrated Sine$_\beta$ point process. This point process arises as the bulk scaling limit of $\beta$-ensembles and has a geometric description through the Brownian carousel, as shown by Valk\'o and Vir\'ag…
The goal of the paper is to introduce a new set of tools for the study of discrete and continuous $\beta$-corners processes. In the continuous setting, our work provides a multi-level extension of the loop equations (also called…
It is demonstrated how to use certain family of commutative hypergroups to provide a universal construction of Biane's quantum Bessel processes of all dimensions not smaller than 1. The classical Bessel processes BES$(\delta)$ are…
For arbitrary $\beta > 0$, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi $\beta$ ensembles. We identify the distribution of these…
We study the twirling semigroups of (super)operators, namely, certain quantum dynamical semigroups that are associated, in a natural way, with the pairs formed by a projective representation of a locally compact group and a convolution…
Recent work has proposed a method for imposing T-duality on the metric, $B$-field, and dilaton of the classical effective action of string theory without using Kaluza-Klein reduction. Specifically, the $D$-dimensional effective action…
We define a new diffusive matrix model converging towards the $\beta$-Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental…