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The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit…

Statistics Theory · Mathematics 2023-05-30 Marija Cuparić , Bojana Milošević , Marko Obradović

In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.

Discrete Mathematics · Computer Science 2008-07-23 J. Diaz , D. Mitsche , X. Perez

Bessel-type convolution algebras of bounded Borel measures on the matrix cones of positive semidefinite $q\times q$-matrices over $\mathbb R, \mathbb C, \mathbb H$ were introduced recently by R\"osler. These convolutions depend on some…

Classical Analysis and ODEs · Mathematics 2012-01-18 Michael Voit

In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…

Probability · Mathematics 2010-06-29 Bela Bollobas , Svante Janson , Oliver Riordan

The aim of this article is to propose a novel kernel estimator of the baseline function in a general high-dimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the…

Applications · Statistics 2015-07-07 Agathe Guilloux , Sarah Lemler , Marie-Luce Taupin

We consider the asymptotics of the discrete heat kernel on isoradial graphs for the case where the time and the edge lengths tend to zero simultaneously. Depending on the asymptotic ratio between time and edge lengths, we show that two…

Probability · Mathematics 2024-01-24 Simon Schwarz , Anja Sturm , Max Wardetzky

This paper studies random lozenge tilings of general non-convex polygonal regions. We show that the pairwise interaction of the non-convexities leads asymptotically to new kernels and thus to new statistics for the tiling fluctuations. The…

Mathematical Physics · Physics 2018-11-21 Mark Adler , Kurt Johansson , Pierre van Moerbeke

We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly…

Analysis of PDEs · Mathematics 2025-02-11 Xiandong Lin , Hailong Ye , Xiao-Qiang Zhao

We investigate the asymptotic behaviour of large eigenvalues for a class of finite difference self-adjoint operators with compact resolvent in $l^2$.

Spectral Theory · Mathematics 2015-06-05 Anne Boutet de Monvel , Jan Janas , Lech Zielinski

We consider the kernel of a hypoelliptic diffusion beyond the case of sub-ellipticity or polynomial coefficients. We get a full asymptotic expansion for small times, based on a Duhamel-type comparison with an approximate polynomial kernel.…

Analysis of PDEs · Mathematics 2023-01-18 Pierre Perruchaud

The aim of this paper is to give fine asymptotics for random variables with moments of Gamma type. Among the examples we consider are random determinants of Laguerre and Jacobi beta ensembles with varying dimensions (the number of observed…

Probability · Mathematics 2017-10-19 Peter Eichelsbacher , Lukas Knichel

Let L be a positive line bundle on a projective complex manifold. We study the asymptotic behavior of Bergman kernels associated with the tensor powers L^p of L as p tends to infinity. The emphasis is the dependence of the uniform estimates…

Complex Variables · Mathematics 2017-06-14 Tien-Cuong Dinh , Xiaonan Ma , Viet-Anh Nguyen

Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems abd determines the…

Functional Analysis · Mathematics 2024-09-24 Gordon Blower

For a wide class of Hermitian random matrices, the limit distribution of the eigenvalues close to the largest one is governed by the Airy point process. In such ensembles, the limit distribution of the k-th largest eigenvalue is given in…

Mathematical Physics · Physics 2017-09-06 Tom Claeys , Antoine Doeraene

We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that…

Statistics Theory · Mathematics 2014-11-05 Markus Bibinger , Per A. Mykland

We calculate the Hankel determinants of sequences of Bernoulli polynomials. This corresponding Hankel matrix comes from statistically estimating the variance in nonparametric regression. Besides its entries' natural and deep connection with…

Number Theory · Mathematics 2021-12-20 Lin Jiu , Ye Li

Modern deep learning models employ considerably more parameters than required to fit the training data. Whereas conventional statistical wisdom suggests such models should drastically overfit, in practice these models generalize remarkably…

Machine Learning · Statistics 2020-08-18 Ben Adlam , Jeffrey Pennington

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…

Probability · Mathematics 2017-02-23 Cagri Sert

We investigate a new type of approximation to quantum determinants, the ``\qFd", and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the \qS…

In this paper, we develop a new scaling method to study spectral and Bergman kernels for the k-th tensor power of a line bundle over a complex manifold under local spectral gap condition. In particular, we establish a simple proof of the…

Complex Variables · Mathematics 2023-10-13 Yueh-Lin Chiang