相关论文: GICAR algebras and dynamics on determinantal point…
The aim of this paper is threefold. Firstly, we develop the author's previous work on the dynamical relationship between determinantal point processes and CAR algebras. Secondly, we present a novel application of the theory of stochastic…
We present a list of algebraic, combinatorial, and analytic mechanisms that give rise to determinantal point processes.
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees).…
Polynomial ensembles are determinantal point processes associated with (non necessarily orthogonal) projections onto polynomial subspaces. The aim of this survey article is to put forward the use of recurrence coefficients to obtain the…
Determinantal point processes on a measure space X whose kernels represent trace class Hermitian operators on L^2(X) are associated to "quasifree" density operators on the Fock space over L^2(X).
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…
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…
We construct the equilibrium Glauber and Kawasaki dynamics on discrete spaces which leave invariant certain determinantal point processes. We will construct Fellerian Markov processes with specified core for the generators. Further, we…
We distinguish a class of random point processes which we call Giambelli compatible point processes. Our definition was partly inspired by determinantal identities for averages of products and ratios of characteristic polynomials for random…
We construct a canonical embedding of the space $L^2$ over a determinantal point process to the fermionic Fock space. Equivalently, we show that a determinantal process is the spectral measure for some explicit commutative group of Gaussian…
For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
The paper deals with a 3-parameter family of probability measures on the set of partitions, called the z-measures. The z-measures first emerged in connection with the problem of harmonic analysis on the infinite symmetric group. They are a…
We introduce and study a class of determinantal probability measures generalising the class of discrete determinantal point processes. These measures live on the Grassmannian of a real, complex, or quaternionic inner product space that is…
The (BC type) z-measures are a family of four parameter $z, z', a, b$ probability measures on the path space of the nonnegative Gelfand-Tsetlin graph with Jacobi-edge multiplicities. We can interpret the $z$-measures as random point…
We consider a family {P} of determinantal point processes arising in representation theory and random matrix theory. The processes live on the one-dimensional lattice and their correlation kernels correspond to projection operators in the…
The main result of this paper is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact…
We consider semisimple triangular operators acting in the symmetric component of the group algebra over the weight lattice of a root system. We present a determinantal formula for the eigenbasis of such triangular operators. This…