English
Related papers

Related papers: Large gap asymptotics for Airy kernel determinants…

200 papers

Determinantal Point Processes (DPPs) are popular models for point processes with repulsion. They appear in numerous contexts, from physics to graph theory, and display appealing theoretical properties. On the more practical side of things,…

Statistics Theory · Mathematics 2018-08-22 Simon Barthelmé , Pierre-Olivier Amblard , Nicolas Tremblay

We study random skew 3D partitions weighted by $q^{\textup{vol}}$ and, specifically, the $q\to 1$ asymptotics of local correlations near various points of the limit shape. We obtain sine-kernel asymptotics for correlations in the bulk of…

Combinatorics · Mathematics 2007-05-23 Andrei Okounkov , Nicolai Reshetikhin

The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by integrals in which the exponents have a…

Probability · Mathematics 2007-05-23 Craig A. Tracy , Harold Widom

We consider an abstract determinantal point process on a general non--elementary Gromov hyperbolic metric space governed by an orthogonal projection in the case when the space is homogeneous and the point process is invariant under…

Probability · Mathematics 2025-03-26 Pierre Lazag

Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, we obtain large-time asymptotic expansions in large…

Probability · Mathematics 2019-07-26 Xuefeng Gao , Lingjiong Zhu

We consider $n$ eigenvalues of complex and symplectic induced spherical ensembles, which can be realised as two-dimensional determinantal and Pfaffian Coulomb gases on the Riemann sphere under the insertion of point charges. For both cases,…

Mathematical Physics · Physics 2024-05-02 Sung-Soo Byun , Seongjae Park

We consider determinantal Coulomb gas ensembles with a class of discrete rotational symmetric potentials whose droplets consist of several disconnected components. Under the insertion of a point charge at the origin, we derive the…

Mathematical Physics · Physics 2022-10-11 Sung-Soo Byun , Meng Yang

We study determinantal random point processes on a compact complex manifold X associated to an Hermitian metric on a line bundle over X and a probability measure on X. Physically, this setup describes a free fermion gas on X subject to a…

Complex Variables · Mathematics 2011-06-27 Robert J. Berman

I derive a Fredholm determinant for the thermal correlator of vertex operators with a conformally invariant density matrix and nonlinear time evolution. Using the method of nonlinear steepest descent I find the long time asymptotics at…

Quantum Gases · Physics 2017-08-08 Tom Price

Determinantal point processes (DPPs) are well-suited for modeling repulsion and have proven useful in many applications where diversity is desired. While DPPs have many appealing properties, such as efficient sampling, learning the…

Machine Learning · Statistics 2014-02-21 Raja Hafiz Affandi , Emily B. Fox , Ryan P. Adams , Ben Taskar

We consider meromorphic transforms given by meromorphic kernels and study their asymptotic expansions under a certain rescaling. Under decay assumptions we establish the full asymptotic expansion in the rescaling parameter of these…

Quantum Algebra · Mathematics 2020-12-22 Jørgen Ellegaard Andersen

We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C^+ associated with the ax+b (affine) group, depending on an admissible Hardy function {\psi}. We obtain the asymptotic behavior of the…

Probability · Mathematics 2022-10-18 Luis Daniel Abreu , Peter Balazs , Smiljana Jakšić

The Gamma kernel is a projection kernel of the form (A(x)B(y)-B(x)A(y))/(x-y), where A and B are certain functions on the one-dimensional lattice expressed through Euler's Gamma function. The Gamma kernel depends on two continuous…

Probability · Mathematics 2013-03-04 Grigori Olshanski

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

Seismic networks provide data that are used as basis both for public safety decisions and for scientific research. Their configuration affects the data completeness, which in turn, critically affects several seismological scientific targets…

A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…

Statistics Theory · Mathematics 2017-02-06 Alberto J. Coca

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

In this paper, we take the first step towards an extension of the nonlinear steepest descent method of Deift, Its and Zhou to the case of operator Riemann-Hilbert problems. In particular, we provide long range asymptotics for a Fredholm…

Functional Analysis · Mathematics 2007-05-23 Spyridon Kamvissis

We study the asymptotic behaviour of orthogonal polynomials in the complex plane that are associated to a certain normal matrix model. The model depends on a parameter and the asymptotic distribution of the eigenvalues undergoes a…

Mathematical Physics · Physics 2018-08-31 Marco Bertola , José Gustavo Elias Rebelo , Tamara Grava

As the conclusion of a line of investigation undertaken in two previous papers, we compute asymptotic frequencies for the values taken by numerators of differences of consecutive Farey fractions with denominators restricted to lie in…

Number Theory · Mathematics 2009-07-02 Dmitry A. Badziahin , Alan K. Haynes