Related papers: Determinantal point processes and fermions on comp…

The Determinantal Point Process (DPP) is a parameterized model for multivariate binary variables, characterized by a correlation kernel matrix. This paper proposes a closed form estimator of this kernel, which is particularly easy to…

Let $L$ be a holomorphic line bundle on a compact complex manifold $X$ of dimension $n,$ and let $e^{-\phi}$ be a continuous metric on $L.$ Fixing a measure $d\mu$ on $X$ gives a sequence of Hilbert spaces consisting of holomorphic sections…

The aim of this note is to announce some results about the probabilistic and deterministic asymptotic properties of linear groups. The first one is the analogue, for norms of random matrix products, of the classical theorem of Cramer on…

The Large Deviations Principle (LDP) is verified for a homogeneous diffusion process with respect to a Brownian motion $B_t$, $$ X^\eps_t=x_0+\int_0^tb(X^\eps_s)ds+ \eps\int_0^t\sigma(X^\eps_s)dB_s, $$ where $b(x)$ and $\sigma(x)$ are are…

We consider a class of slow-fast processes on a connected complete Riemannian manifold $M$.The limiting dynamics as the scale separation goes to $\infty$ is governed by the averaging principle. Around this limit, we prove large deviation…

The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…

Following the line of \cite{AS} we propose an improved algorithm which allows to calculate a D-dimensional fermion determinant integrating the exponent of D+1 dimensional Hermitean bosonic action. For a finite extra dimension the…

The Airy point process is a determinantal point process that arises from the spectral edge of the Gaussian Unitary Ensemble. In this paper, we establish a large deviation principle for the Airy point process. Our result also extends to…

We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all…

We give natural constructions of number rigid determinantal point processes on the unit disc $\mathbb{D}$ with sub-Bergman kernels of the form \[ K_\Lambda(z, w) = \sum_{n\in \Lambda}(n+1) z^n \bar{w}^n, \quad z, w \in \mathbb{D}, \] with…

Determinantal Point Processes (DPPs) are probabilistic models that arise in quantum physics and random matrix theory and have recently found numerous applications in computer science. DPPs define distributions over subsets of a given ground…

We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert…

In this paper, we propose a new randomized method for numerical integration on a compact complex manifold with respect to a continuous volume form. Taking for quadrature nodes a suitable determinantal point process, we build an unbiased…

The aim of this study is tree-fold. First, we investigate the thermodynamics of the Ising models with respect to 2-multiple Hamiltonians. This extends the previous results of [Chazotte and Redig, Electron. J. Probably., 2014] to…

Although the Poisson point process (PPP) has been widely used to model base station (BS) locations in cellular networks, it is an idealized model that neglects the spatial correlation among BSs. The present paper proposes the use of…

We obtain scaling and local limit results for large random Young tableaux of fixed shape $\lambda^0$ via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove: (1) an explicit…

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…

Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power…

One of the main contributions of this paper is to illustrate how large deviation theory can be used to determine the equilibrium distribution of a basic droplet model that underlies a number of important models in material science and…

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a "pointwise" large deviation principle (LDP) for the full…