Related papers: Forcing quasirandomness with 4-point permutations
Random intersection graphs are characterized by three parameters: $n$, $m$ and $p$, where $n$ is the number of vertices, $m$ is the number of objects, and $p$ is the probability that a given object is associated with a given vertex. Two…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
Let $\mu$ be a positive measure on the real line with locally finite support $\Lambda$ and integer masses such that its Fourier transform in the sense of distributions is a purely point measure. An explicit form is found for an entire…
Quasi-rigidity means that one builds a theory for assemblies of grains under a slowly changing external load by using the deformation of those grains as a small parameter. Is quasi-rigidity a complete theory for these granular assemblies?…
Although nonclassical quantum states are important both conceptually and as a resource for quantum technology, it is often difficult to test whether a given quantum system displays nonclassicality. A simple method to certify nonclassicality…
We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…
We prove a theorem on distortion of cross ratio of four points under the mapping effected by a complex polynomial with restricted critical values. Its corollaries include inequalities involving the absolute value and certain coefficients of…
A permutation sequence $(\sigma_n)_{n \in \mathbb{N}}$ is said to be convergent if, for every fixed permutation $\tau$, the density of occurrences of $\tau$ in the elements of the sequence converges. We prove that such a convergent sequence…
Hyperuniformity is a property of certain heteroneous media in which density fluctuations in the long wavelength range decay to zero. In reciprocal space this behavior translates into a decay of Fourier intensities in the range near small…
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…
We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing…
We consider quasiconformal deformations of $\mathbb{C}\setminus\mathbb{Z}$. We give some criteria for infinitely often punctured planes to be quasiconformally equivalent to $\mathbb{C}\setminus\mathbb{Z}$. In particular, we characterize the…
Consider a square matrix with independent and identically distributed entries of zero mean and unit variance. It is well known that if the entries have a finite fourth moment, then, in high dimension, with high probability, the spectral…
The pantograph differential equation and its solution, the deformed exponential function, are remarkable objects that appear in areas as diverse as combinatorics, number theory, statistical mechanics, and electrical engineering. In this…
In a recent Letter we proposed a means to realize a quasicrystal with eight-fold symmetry by trapping particles in an optical potential created by four lasers. The quasicrystals obtained in this way, which are closely related to the…
For any class $\mathcal{C}$ of bipartite graphs, we define quasi-$\cal C$ to be the class of all graphs $G$ such that every bipartition of $G$ belongs to $\cal C$. This definition is motivated by a generalisation of the switch Markov chain…
We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time--space complexity is roughly quadratic in the logarithm of the…
It is argued that a fuzzy version of 4-truth-valued paraconsistent logic (with truth values corresponding to True, False, Both and Neither) can be approximately isomorphically mapped into the complex-number algebra of quantum probabilities.…
The paper contains an exposition of recent as well as old enough results on determinantal random point fields. We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of the…
Spatial Fourier transforms of quasipatterns observed in Faraday wave experiments suggest that the patterns are well represented by the sum of 8, 10 or 12 Fourier modes with wavevectors equally spaced around a circle. This representation has…