Related papers: The Bessel Line Ensemble
We study the local statistics of orthogonal polynomial ensembles near a hard edge, subject to a multiplicative deformation of the measure. Probabilistically, this deformation corresponds to a position-dependent conditional thinning of the…
A system of non-intersecting squared Bessel processes is considered which all start from one point and they all return to another point. Under the scaling of the starting and ending points when the macroscopic boundary of the paths touches…
The Airy$_\beta$ line ensemble is a random collection of continuous curves, which should serve as a universal edge scaling limit in problems related to eigenvalues of random matrices and models of 2d statistical mechanics. This line…
The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper is to provide a set of tools which allow for precise probabilistic analysis of the…
A new class of random composition structures (the ordered analog of Kingman's partition structures) is defined by a regenerative description of component sizes. Each regenerative composition structure is represented by a process of random…
A Bessel field $\mathcal{B}=\{\mathcal{B}(\alpha,t), \alpha\in\mathbb{N}_0, t\in\mathbb{R}\}$ is a two-variable random field such that for every $(\alpha,t)$, $\mathcal{B}(\alpha,t)$ has the law of a Bessel point process with index…
The Airy$_\beta$ line ensemble is an infinite sequence of random curves. It is a natural extension of the Tracy-Widom$_\beta$ distributions, and is expected to be the universal edge scaling limit of a range of models in random matrix theory…
Bessel process is defined as the radial part of the Brownian motion (BM) in the $D$-dimensional space, and is considered as a one-parameter family of one-dimensional diffusion processes indexed by $D$, BES$^{(D)}$. It is well-known that…
We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be…
The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter $\alpha$. For this point process, we obtain 1) exponential moment…
We investigate the hard edge scaling limit of the ensemble defined by the squared singular values of the product of two coupled complex random matrices. When taking the coupling parameter to be dependent on the size of the product matrix,…
We construct a one-parameter family of infinite line ensembles on $[0, \infty)$ that are natural half-space analogues of the Airy line ensemble. Away from the origin these ensembles are locally described by avoiding Brownian bridges, and…
We provide a new construction of Brownian disks in terms of forests of continuous random trees equipped with nonnegative labels corresponding to distances from a distinguished point uniformly distributed on the boundary of the disk. This…
It is shown that the tessellation of a compact, negatively curved surface induced by a typical long geodesic segment, when properly scaled, looks locally like a Poisson line process. This implies that the global statistics of the…
Consider a stationary Poisson point process in $\mathbb{R}^d$ and connect any two points whenever their distance is less than or equal to a prescribed distance parameter. This construction gives rise to the well known random geometric…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…
Consider N Brownian bridges B_i:[-N,N] -> R, B_i(-N) = B_i(N) = 0, 1 <= i <= N, conditioned not to intersect. The edge-scaling limit of this system is obtained by taking a limit as N -> infinity of these curves scaled around (0,2^{1/2} N)…
Consider a sequence of Gibbsian line ensembles, whose lowest labeled curves (i.e., the edge) have tight one-point marginals. Then, given certain technical assumptions on the nature of the Gibbs property and underlying random walk measure,…
Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory…
The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are given by the multi-line Airy process. It is a natural object in the KPZ universality class: for example, its…