Related papers: Cantor-solus and Cantor-multus Distributions
Cantor sets of integers have a rich set of arithmetic combinatorial properties. We consider classical Cantor sets, with a base and a fixed set of allowed digits. For such sets, we (a) give examples of such sets that satisfy the intersective…
We introduce several statistics on ordered partitions of sets, that is, set partitions where the blocks are permuted arbitrarily. The distribution of these statistics is closely related to the q-Stirling numbers of the second kind. Some of…
Accurate synchrotron transfer coefficients are essential for modeling radiation processes in astrophysics. However, their current calculation methods face significant challenges. Analytical approximations of the synchrotron emissivity,…
We derive functional equations for distributions of six classical statistics (ascents, descents, left-to-right maxima, right-to-left maxima, left-to-right minima, and right-to-left minima) on separable and irreducible separable…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…
Firstly, we propose and investigate a dyadic Cantor set (DCS) and its kinetic counterpart where a generator divides an interval into two equal parts and removes one with probability $(1-p)$. The generator is then applied at each step to all…
The existence of two different Cantor sets, one of them contained in the set of Liouville numbers and the other one inside the set of Diophantine numbers, is proved. Finally, a necessary and sufficient condition for the existence of a…
Imagine a sequence in which the first letter comes from a binary alphabet, the second letter can be chosen on an alphabet with 10 elements, the third letter can be chosen on an alphabet with 3 elements and so on. When such a sequence can be…
The joint probability distribution in the full counting statistics (FCS) for noninteracting electrons is discussed for an arbitrary number of initially separate subsystems which are connected at t=0 and separated at a later time. A simple…
Let $Q=(q_n)_{n=1}^\infty$ be a sequence of bases with $q_i\ge 2$. In the case when the $q_i$ are slowly growing and satisfy some additional weak conditions, we provide a construction of a number whose $Q$-Cantor series expansion is both…
We study properties of the set of subsums for a convergent series $ k_1 \sin x + \dots + k_m \sin x +\dots + k_1\sin x^n +\dots + k_m \sin x^n + \dots $, where $k_1, k_2, k_3,\dots,k_m$ are fixed positive integers and $0<x<1$. Depends on…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…
A quantum key distribution protocol based on entanglement swapping is proposed. Through choosing particles by twos from the sequence and performing Bell measurements, two communicators can detect eavesdropping and obtain the secure key.…
This paper presents the Computoser hybrid probability/rule based algorithm for music composition (http://computoser.com) and provides a reference implementation. It addresses the issues of unpleasantness and lack of variation exhibited by…
The pentagonal number theorem is extended to the sequence of the number of integer partitions with all parts equal. The new pentagonal number theorem implies that the distribution of the primes is just a specific detail of the application…
Waiting time distribution and the zero-frequency full counting statistics of unidirectional electron transport through a double quantum dot molecule attached to spin-polarized leads are analyzed using the quantum master equation. The…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
There are two methods for counting the number of occurrences of a string in another large string. One is to count the number of places where the string is found. The other is to determine how many pieces of string can be extracted without…
In this paper, we study $C^{\zeta}$-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or…
We develop the resource theory of private randomness extraction in the distributed and device-dependent scenario. We begin by introducing the notion of independent random bits, which are bipartite states containing ideal private randomness…