Related papers: Gibbs Ensembles of Nonintersecting Paths

We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core…

We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…

In this paper, we show how general determinants may be viewed as generating functions of nonintersecting lattice paths, using the Lindstr\"om-Gessel-Viennot interpretation of semistandard Young tableaux and the Jacobi-Trudi identity…

Bordered and framed Toeplitz/Hankel determinants have the same structure as Toeplitz/Hankel determinants except in small number of matrix rows and/or columns. We review these structured determinants and their connections to orthogonal…

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label…

Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Indeed, many popular nonparametric priors, such as…

We study some random interlaced configurations considering the eigenvalues of the main minors of Hermitian random matrices of the classical complex Lie algebras. We claim that these random configurations are determinantal and give their…

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…

A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…

We study the convergence of distributions on finite paths of weighted digraphs, namely the family of Boltzmann distributions and the sequence of uniform distributions. Targeting applications to the convergence of distributions on paths, we…

Consider $a$ particles performing simple, symmetric, non-intersecting random walks, starting at points $2(j-1)$, $1\le j\le a$ at time 0 and ending at $2(j-1)+c-b$ at time $b+c$. This can also be interpreted as a random rhombus tiling of an…

Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…

We introduce random matrix ensembles that correspond to the infinite families of irreducible Riemannian symmetric spaces of type I. In particular, we recover the Circular Orthogonal and Symplectic Ensembles of Dyson, and find other families…

For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…

This work lies at the intersection of Gibbs models and hyperuniform point processes. Classical Gibbs models, whether defined on lattices or in continuous space, provide flexible tools to describe interacting particle systems but are…

A family of random variables $\mathbf{X}(s)$, depending on a real parameter $s>-\frac{1}{2}$, appears in the asymptotics of the joint moments of characteristic polynomials of random unitary matrices and their derivatives, in the ergodic…

The purpose of this work is to expand and clarify the concept of the class of Gibbs random fields and give its structure the form accepted in the theory of random processes. It is possible thanks to the proposed purely probabilistic…

We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…

The Gibbs point processes (GPP) constitute a large class of point processes with interaction between the points. The interaction can be attractive, repulsive, depending on geometrical features whereas the null interaction is associated to…

We provide a Poisson approximation result for dependent thinnings of Gibbs point processes as well as qualitative and quantitative central limit theorems for geometric functionals of Gibbs point processes in increasing observation windows.…