Related papers: The bead process for beta ensembles
In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the…
In this paper, we study the phenomenon of coming down from infinity for subcritical cooperative branching processes with pairwise interactions (BPI processes) under suitable conditions. BPI processes are continuous-time Markov chains that…
The jigsaw percolation process, introduced by Brummitt, Chatterjee, Dey and Sivakoff, was inspired by a group of people collectively solving a puzzle. It can also be seen as a measure of whether two graphs on a common vertex set are…
We prove a general inequality on $\beta$-mixing coefficients of point processes depending uniquely on their $n$-th order intensity functions. We apply this inequality in the case of determinantal point processes and show that the rate of…
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…
The bead model is a random point field on $\mathbb{Z}\times\mathbb{R}$ which can be viewed as a scaling limit of dimer model. We prove that, in the scaling limit, the normalized height function of a uniformly chosen random bead…
We study a family of periodically weighted Aztec diamond dimer models near their turning points. We establish that, asymptotically, as $N\rightarrow\infty$, their fluctuations there, scaled by $\sqrt{N}$, are described by a marked…
Bessel processes associated with the root systems $A_{N-1}$ and $B_N$ describe interacting particle systems with $N$ particles on $\mathbb R$; they form dynamic versions of the classical $\beta$-Hermite and Laguerre ensembles. In this paper…
We use generalized beta integrals to construct examples of Markov processes with linear regressions, and quadratic second conditional moments.
The "necklace process", a procedure constructing necklaces of black and white beads by randomly choosing positions to insert new beads (whose color is uniquely determined based on the chosen location), is revisited. This article illustrates…
We study the scaling limit of the spectrum of the \beta-Jacobi ensemble at the soft-edge and hard-edge for general values of \beta. We show that the limiting point processes correspond respectively to the stochastic Airy and Bessel point…
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. Motivated by the functional estimation of the density of the…
Multivariate Bessel processes $(X_{t,k})_{t\ge0}$ describe interacting particle systems of Calogero-Moser-Sutherland type and are related with $\beta$-Hermite and $\beta$-Laguerre ensembles. They depend on a root system and a multiplicity…
We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by B\'erard and Gou\'er\'e (2010). The proof is based on a connection with a supercritical Galton-Watson process…
The beta process has recently been widely used as a nonparametric prior for different models in machine learning, including latent feature models. In this paper, we prove the asymptotic consistency of the finite dimensional approximation of…
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 to general values of $\beta>0$ through…
We develop a coordinate-free probabilistic framework for determinantal point processes associated with Bergman kernels on compact complex manifolds. The basic issue is that Bergman kernels are naturally line-bundle-valued:…
Bourgade, Nikeghbali and Rouault recently proposed a matrix model for the circular Jacobi $\beta$-ensemble, which is a generalization of the Dyson circular $\beta$-ensemble but equipped with an additional parameter $b$, and further studied…
The Bayesian transformed Gaussian process (BTG) model, proposed by Kedem and Oliviera, is a fully Bayesian counterpart to the warped Gaussian process (WGP) and marginalizes out a joint prior over input warping and kernel hyperparameters.…
We introduce a broad class of self-similar processes $\{Z(t),t\ge 0\}$ called generalized Hermite process. They have stationary increments, are defined on a Wiener chaos with Hurst index $H\in (1/2,1)$, and include Hermite processes as a…