相关论文: The Pair Correlation Function of Multi-Dimensional…

We introduce a generic framework to provide bounds related to the pair correlation of sequences belonging to a wide class. We consider analogues of Montgomery's form factor for zeros of the Riemann zeta function in the case of arbitrary…

We consider the Poisson cylinder model in ${\mathbb R}^d$, $d\ge 3$. We show that given any two cylinders ${\mathfrak c}_1$ and ${\mathfrak c}_2$ in the process, there is a sequence of at most $d-2$ other cylinders creating a connection…

Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…

For a field $\mathbb{F}$ and integers $d, k$ and $\ell$, a set $A \subseteq \mathbb{F}^d$ is called $(k,\ell)$-nearly orthogonal if all vectors in $A$ are non-self-orthogonal and every $k+1$ vectors in $A$ contain $\ell + 1$ pairwise…

Motivated by the Berry-Tabor Conjecture and the seminal work of Rudnick-Sarnak, the fine-scale properties of sequences $(a_n\alpha)_{n \in \mathbb{N}} \mod 1$ with $(a_n)_{n \in \mathbb{N}} \subseteq \mathbb{N} $ and $\alpha$ irrational…

$\newcommand{\Re}{\mathbb{R}}$We study the minWSPD problem of computing the minimum-size well-separated pairs decomposition of a set of points, and show constant approximation algorithms in low-dimensional Euclidean space and doubling…

We study independent long-range percolation on $\mathbb{Z}^d$ where the vertices $u$ and $v$ are connected with probability asymptotic to $\frac{\beta}{\|u-v\|^{2d}}$ for $\|u-v\|_\infty\geq 2$ and with probability 1 for $\|u-v\|_\infty=1$,…

A recent Bose-Einstein condensation (BEC) model of several cuprate superconductors is based on bosonic Cooper pairs (CPs) moving in 3D with a quadratic energy-momentum (dispersion) relation. The 3D BEC condensate-fraction vs. temperature…

Goldston and Montgomery [3] proved that the Strong Pair Correlation Conjecture and two second moments of primes in short intervals are equivalent to each other under Riemann Hypothesis. In this paper, we get the second main terms for each…

We present the results of a quantum Monte Carlo study of the extended $s$ and the $d_{x^2-y^2}$ pairing correlation functions for the two-dimensional Hubbard model, computed with the constrained-path method. For small lattice sizes and weak…

Polarity coincidence correlator (PCC), when used to estimate the covariance matrix on an element-by-element basis, may not yield a positive semi-definite (PSD) estimate. Devlin et al. [1], claimed that element-wise PCC is not guaranteed to…

Distributional approximations of (bi--) linear functions of sample variance-covariance matrices play a critical role to analyze vector time series, as they are needed for various purposes, especially to draw inference on the dependence…

We define a notion of Poissonian pair correlation (PPC) for Riemannian manifolds without boundary and prove that PPC implies uniform distribution in this setting. This extends earlier work by Grepstad and Larcher, Aistleitner, Lachmann, and…

The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…

Suppose that two large, multi-dimensional data sets are each noisy measurements of the same underlying random process, and principle components analysis is performed separately on the data sets to reduce their dimensionality. In some…

The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers [RW08, ORW08]. In this paper we study the correlation structure among different functionals such as nodal…

We consider the problem of calculating distance correlation coefficients between random vectors whose joint distributions belong to the class of Lancaster distributions. We derive under mild convergence conditions a general series…

We consider the performance of the bootstrap in high-dimensions for the setting of linear regression, where $p<n$ but $p/n$ is not close to zero. We consider ordinary least-squares as well as robust regression methods and adopt a minimalist…

For $s \geq 0$ and a parameter $0 < \beta < 1$, the weak pair correlation function $f_{N,\beta}(s)$ for the first $N \in \mathbb{N}$ elements of a sequence $(x_n)_{n \in \mathbb{N}} \subset[0,1]$ is evidently non-decreasing in $s$.…

We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions $d\ge 2$. In previous works we studied the model problem of a discrete elliptic equation on $\mathbb{Z}^d$. Under the…