Related papers: Determinantal point processes and fermion quasifre…

With view to applications in stochastic analysis and geometry, we introduce a new correspondence for positive definite kernels (p.d.) $K$ and their associated reproducing kernel Hilbert spaces. With this we establish two kinds of…

We obtain large gap asymptotics for Airy kernel Fredholm determinants with any number $m$ of discontinuities. These $m$-point determinants are generating functions for the Airy point process and encode probabilistic information about…

We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…

Determinantal point processes (DPPs) have attracted significant attention as an elegant model that is able to capture the balance between quality and diversity within sets. DPPs are parameterized by a positive semi-definite kernel matrix.…

For a locally finite point set $\Lambda \subset \mathbb{R}$, consider the collection of exponential functions given by $\mathcal{E}_{\Lambda}:= \{e^{i \lambda x} : \lambda \in L \}$. We examine the question whether $\mathcal{E}_{\Lambda}$…

When the number of particles is finite, the noncolliding Brownian motion (the Dyson model) and the noncolliding squared Bessel process are determinantal diffusion processes for any deterministic initial configuration $\xi=\sum_{j \in…

We use a support vector regressor based on a projected quantum kernel method to predict the density structure of 1D fermionic systems of interest in quantum chemistry and quantum matter. The kernel is built on with the observables of a…

We address the question of identifying degrees of freedom for quantum systems. Typically, quasi-particle descriptions of correlated matter are based upon the canonical algebras of bosons or fermions. Here we highlight that a special class…

Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel $K$ that can be seen as a matrix storing the similarity between points. The diversity comes…

Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and determinantal point processes. Her initial motivation was to provide models for the set of detection times in fundamental bosonic or fermionic optical…

In the study of stochastic systems, the committor function describes the probability that a system starting from an initial configuration $x$ will reach a set $B$ before a set $A$. This paper introduces an efficient and interpretable…

Positive and negative dependence are fundamental concepts that characterize the attractive and repulsive behavior of random subsets. Although some probabilistic models are known to exhibit positive or negative dependence, it is challenging…

We study a 3-parametric family of stochastic point processes on the one-dimensional lattice originated from a remarkable family of representations of the infinite symmetric group. We prove that the correlation functions of the processes are…

Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in…

We study the problem raised in [Marco Stevens, Equivalent symmetric kernels of determinantal point processes, RMTA, 10(03):2150027, 2021] concerning the extension of its main result to the more general (potentially non-symmetric) setting.…

We prove a local central limit theorem (LCLT) for the number of points $N(J)$ in a region $J$ in $\mathbb R^d$ specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of $N(J)$ tends to…

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…

We study the hermitian one matrix model with semi-classical potential. This is a general unitary invariant random matrix ensemble in which the potential has a derivative that is a rational function and the measure is supported on some…

In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its…

We study a family of Fredholm determinants associated to deformations of the sine kernel, parametrized by a weight function w. For a specific choice of w, this kernel describes bulk statistics of finite temperature free fermions. We…