Related papers: An Explicit non-Poissonian Pair Correlation Functi…
We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph's spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…
Aperiodic autocorrelation is an important indicator of performance of sequences used in communications, remote sensing, and scientific instrumentation. Knowing a sequence's autocorrelation function, which reports the autocorrelation at…
We study correlation bounds under pairwise independent distributions for functions with no large Fourier coefficients. Functions in which all Fourier coefficients are bounded by $\delta$ are called $\delta$-{\em uniform}. The search for…
Pair densities and associated correlation functions provide a critical tool for introducing many-body correlations into a wide-range of effective theories. Ab initio calculations show that two-nucleon pair-densities exhibit strong spin and…
We prove an abstract result on the correlations of pairs of elements in an exponentially growing discrete subset $\mathcal E$ of $[0,+\infty[\,$ endowed with a weight function. Assume that there exist $\alpha\in\mathbb R$, $c,\delta>0$ such…
We show the convergence of the characteristic polynomial for random permutation matrices sampled from the generalized Ewens distribution. Under this distribution, the measure of a given permutation depends only on its cycle structure,…
Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…
We study estimation of an $s$-sparse signal in the $p$-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely the rate scales with respect to…
$k$-level correlation is a local statistic of sequences modulo 1, describing the local spacings of $k$-tuples of elements. For $k = 2$ this is also known as pair correlation. We show that there exists a well spaced increasing sequence of…
One possible way to investigate the nature of the primordial power spectrum fluctuations is by investigating the statistical properties of the local maximum in the density fluctuation fields. In this work we present a study of the mean…
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
We prove the convergence of moments of the number of directions of affine lattice vectors that fall into a small disc, under natural Diophantine conditions on the shift. Furthermore, we show that the pair correlation function is Poissonian…
We study the problem of constructing sequences $(x_n)_{n=1}^{\infty}$ on $[0,1]$ in such a way that $$ D_N^* = \sup_{0 \leq x \leq 1} \left| \frac{ \left\{1 \leq i \leq N: x_i \leq x \right\}}{N} - x \right|$$ is uniformly small. A result…
We present a unified framework to study threshold functions for the existence of solutions to linear systems of equations in random sets which includes arithmetic progressions, sum-free sets, $B_{h}[g]$-sets and Hilbert cubes. In…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Using a proposed generalization of the pair distribution function for a gas of non-interacting particles obeying fractional exclusion statistics in arbitrary dimensionality, we derive the statistical correlations in the asymptotic limit of…
The decreasing enumeration of the points of a Poisson random measure whose mean measure has finite survival function on the positive half-axis can be represented as a non-increasing function of the jump times of a standard Poisson process.…
We enumerate arrangements of $n$ couples, i.e. pairs of people, placed in a single-file queue, and consider four statistics from the vantage point of a distinguished given couple. In how many arrangements are exactly $p$ of the $n-1$ other…