Related papers: A length characterization of $*$-spread
The discrete distribution of the length of longest increasing subsequences in random permutations of $n$ integers is deeply related to random matrix theory. In a seminal work, Baik, Deift and Johansson provided an asymptotics in terms of…
Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…
Given a network and a set of vertices called seeds to initially inject information, influence spread is the expected number of vertices that eventually receive the information under a certain stochastic model of information propagation.…
In this paper we consider a model for the diffusion of a population in a strip-shaped field, where the growth of the species is governed by a Fisher-KPP equation and which is bounded on one side by a road where the species can have a…
It is argued that there are characteristic intervals associated with any particle that can be derived without reference to the speed of light $c$. Such intervals are inferred from zeros of wavefunctions which are solutions to the…
Formula for the size of the scatterer is derived explicitly in terms of the scattering amplitude corresponding to this scatterer. By the scatterer either a bounded obstacle $D$ or the support of the compactly supported potential is meant
We present a method to characterize the distribution of length-scales of finite, disordered patterns with, on average, radial symmetry. This method makes it possible to quantify the distribution of characteristic length scales in cases…
We introduce a sieve for counting twin primes up to a given range. Our method depends on a parameter ${\lambda}_x$ and the estimation of the number of twin primes obtained as a result, is called a fundamental structure of the distribution…
In this work we show that the prime distribution is deterministic. Indeed the set of prime numbers P can be expressed in terms of two subsets of N using three specific selection rules, acting on two sets of prime candidates. The prime…
A well-known conjecture asserts that, for any given positive real number $\lambda$ and nonnegative integer $m$, the proportion of positive integers $n \le x$ for which the interval $(n,n + \lambda\log n]$ contains exactly $m$ primes is…
We examine a family of discrete probability distributions that describes the "spillage number" in the extended balls-in-bins model. The spillage number is defined as the number of balls that occupy their bins minus the total number of…
Universal source coding at short blocklengths is considered for an exponential family of distributions. The \emph{Type Size} code has previously been shown to be optimal up to the third-order rate for universal compression of all memoryless…
We prove a limit theorem for the the maximal interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit ball of dimension 2 or more. The exact form of the limit distribution and the required normalisation are…
Let $H$ be a Krull monoid with finite class group $G$ such that every class contains a prime divisor. Then every non-unit $a \in H$ can be written as a finite product of atoms, say $a=u_1 \cdot \ldots \cdot u_k$. The set $\mathsf L (a)$ of…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities…
Generalized Maxwell distribution is an extension of the classic Maxwell distribution. In this paper, we concentrate on the joint distributional asymptotics of normalized maxima and minima. Under optimal normalizing constants, asymptotic…
We say that a C*-algebra is nowhere scattered if none of its quotients contains a minimal open projection. We characterize this property in various ways, by topological properties of the spectrum, by divisibility properties in the Cuntz…