English
Related papers

Related papers: Determinantal point processes and fermion quasifre…

200 papers

Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional…

Probability · Mathematics 2014-07-01 Tvrtko Tadić

In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential…

Statistics Theory · Mathematics 2018-05-01 Ansgar Steland

A determinantal point process is a stochastic point process that is commonly used to capture negative correlations. It has become increasingly popular in machine learning in recent years. Sampling a determinantal point process however…

Numerical Analysis · Mathematics 2020-09-02 Lexing Ying

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…

Probability · Mathematics 2025-04-18 Ryosuke Sato

The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these…

Statistical Mechanics · Physics 2009-11-13 A. Scardicchio , C. E. Zachary , S. Torquato

We find the transition kernels for four Markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin-McGregor type kernel. The resulting kernels all inherit the determinantal…

Probability · Mathematics 2008-12-06 A. B. Dieker , J. Warren

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…

Machine Learning · Statistics 2025-05-21 Christian Gouriéroux , Yang Lu

We study determinantal point processes on $\mathbb{C}$ induced by the reproducing kernels of generalized Fock spaces as well as those on the unit disc $\mathbb{D}$ induced by the reproducing kernels of generalized Bergman spaces. In the…

Probability · Mathematics 2016-12-01 Alexander I. Bufetov , Yanqi Qiu

We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set…

Probability · Mathematics 2008-03-02 Alexei Borodin , Grigori Olshanski

Let $F$ be a non-discrete non-Archimedean local field. For any subset $S\subset F$ with finite Haar measure, there is a stationary determinantal point process on $F$ with correlation kernel $\widehat{\mathbb{1}}_S(x-y)$, where…

Probability · Mathematics 2017-02-24 Yanqi Qiu

We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distribution of eigenvalues of large random Hermitian matrices near…

Mathematical Physics · Physics 2024-02-20 Shuai-Xia Xu , Shu-Quan Zhao , Yu-Qiu Zhao

Determinantal process is a dynamical extension of a determinantal point process such that any spatio-temporal correlation function is given by a determinant specified by a single continuous function called the correlation kernel.…

Probability · Mathematics 2013-07-10 Makoto Katori

It is known that determinantal point processes have an intimate relation to operator algebras. In the paper, we extend this relationship to encompass dynamical aspects. Especially, we delve into two types of determinantal point processes.…

Operator Algebras · Mathematics 2023-09-06 Ryosuke Sato

We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young diagram and in the intermediate zone between the diagonal and…

Mathematical Physics · Physics 2007-05-23 Alexei Borodin , Grigori Olshanski

Introduced by Okounkov and Reshetikhin, the Schur process is known to be a determinantal point process, meaning that its correlation functions are minors of a single correlation kernel matrix. Previously, this was derived using…

Combinatorics · Mathematics 2023-10-10 Amol Aggarwal

A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures, whose correlation functions are all given by determinants specified by an integral kernel called the correlation kernel. First we show…

Probability · Mathematics 2020-03-11 Makoto Katori

The main result of this paper, Theorem 1.5, establishes a conjecture of Lyons and Peres: for a determinantal point process governed by a reproducing kernel, the system of kernels sampled at the particles of a random configuration is…

Probability · Mathematics 2018-12-19 Alexander I. Bufetov , Yanqi Qiu , Alexander Shamov

A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures $\Xi$ on a space $S$ with measure $\lambda$, whose correlation functions are all given by determinants specified by an integral kernel…

Probability · Mathematics 2021-09-08 Makoto Katori , Tomoyuki Shirai

The paper contains an exposition of recent as well as old enough results on determinantal random point fields. We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of the…

Probability · Mathematics 2015-06-26 Alexander Soshnikov

Determinantal processes provide mathematical modeling of repulsion among points. In quantum mechanics, Slater determinant states generate such processes, reflecting Fermionic behavior. This note exploits the connections between the former…

Mathematical Physics · Physics 2026-03-26 Chiara Boccato , Francesca Pieroni , Dario Trevisan