相关论文: The Pair Correlation Function of Multi-Dimensional…
Mean field approach, although a generally reliable tool that captures major short range correlations, often fails in symmetric low dimensional strongly correlated electronic systems like those described by the Hubbard model. In these…
A sequence $(x_n)$ on the torus is said to have Poissonian pair correlations if $\# \{1\le i\neq j\le N: |x_i-x_j| \le s/N\}=2sN(1+o(1))$ for all reals $s>0$, as $N\to \infty$. It is known that, if $(x_n)$ has Poissonian pair correlations,…
It is shown that short-range correlations between large prime numbers (~10^5 and larger) have a Poissonian nature. Correlation length \zeta = 4.5 for the primes ~10^5 and it is increasing logarithmically according to the prime number…
We establish Poisson and compound Poisson approximations for stabilizing statistics of $\beta$-mixing point processes and give explicit rates of convergence. Our findings are based on a general estimate of the total variation distance of a…
George R. Terrell (1983, {Ann. Probab., vol. 11(3), pp. 823--826) showed that the Pearson coefficient of correlation of an ordered pair from a random sample of size two is at most one-half, and the equality is attained only for rectangular…
Z. Rudnick and P. Sarnak have proved that the pair correlation for the fractional parts of $n^2 \alpha$ is Poissonian for almost all $\alpha$. However, they were not able to find a specific $\alpha$ for which it holds. We show that the…
In the present paper we prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure $\mu$ on the $d$-dimensional unit cube. We improve a theorem of Beck, by showing that for…
In this article we prove that if the additive energy of a strictly increasing sequence $(a_n)$ of natural numbers is less than $N^3/(\log N)^C$ for some $C\geq13.155$, then $(\{a_n\alpha\})$ has Poissonian pair correlation for almost all…
In this paper we consider the fractional parts of a general sequence, for example the sequence $\alpha \sqrt{n}$ or $\alpha n^2$. We give a general method, which allows one to show that long-range correlations (correlations where the…
The recent results of [J. Dubail, J.-M. St\'ephan, J. Viti, P. Calabrese, Scipost Phys. 2, 002 (2017)], which aim at providing access to large scale correlation functions of inhomogeneous critical one-dimensional quantum systems -- e.g. a…
Ingrid Carbone introduced the notion of so-called LS-sequences of points, which are obtained by a generalization of Kakutani's interval splitting procedure. Under an appropriate choice of the parameters $L$ and $S$, such sequences have low…
We present a method to obtain sets of vectors proving the Bell-Kochen-Specker theorem in dimension $n$ from a similar set in dimension $d$ ($3\leq d<n\leq 2d$). As an application of the method we find the smallest proofs known in dimension…
Pairwise likelihood is a useful approximation to the full likelihood function for covariance estimation in high-dimensional context. It simplifies high-dimensional dependencies by combining marginal bivariate likelihood objects, thus making…
We study the statistics of pairs from the sequence $(n^\alpha)_{n\in\mathbb{N}^*}$, for every parameter $\alpha \in \, ]0,1[$. We prove the convergence of the empirical pair correlation measures towards a measure with an explicit density.…
Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional…
In this paper, we follow the recent work of Helleseth, Kholosha, Johanssen and Ness to study the cross correlation between an $m$-sequence of period $2^m-1$ and the $d$-decimation of an $m$-sequence of shorter period $2^{n}-1$ for an even…
We show that the high-dimensional behavior of symmetrically penalized least squares with a possibly non-separable, symmetric, convex penalty in both (i) the Gaussian sequence model and (ii) the linear model with uncorrelated Gaussian…
The distances between flats of a Poisson $k$-flat process in the $d$-dimensional Euclidean space with $k<d/2$ are discussed. Continuing an approach originally due to Rolf Schneider, the number of pairs of flats having distance less than a…
Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…
The purpose of this note is to present a construction of sequences which do not have metric Poissonian pair correlations (MPPC) and whose additive energies grow at rates that come arbitrarily close to a threshold below which it is believed…