相关论文: Poisson generic sequences

Denote by $\mathbb{N}$ and $\mathbb{P}$ the set of all positive integers and prime numbers, respectively. Let $\mathbb{P}=\{p_1<p_2<\dots <p_n<\dots\}$, where $p_n$ is the $n$-th prime number. For $k\in\mathbb{N}$ we recursively define…

In this article, we study critical points (zeros of derivative) of random polynomials. Take two deterministic sequences $\{a_n\}_{n\geq1}$ and $\{b_n\}_{n\geq1}$ of complex numbers whose limiting empirical measures are same. By choosing…

We count various classes of algebraic integers of fixed degree by their largest absolute value. The classes of integers considered include all algebraic integers, Perron numbers, totally real integers, and totally complex integers. We give…

Let $E$ be an elliptic curve defined over rational field $\mathbb{Q}$ and $N$ be a positive integer. Now, $M_E(N)$ denotes the number of primes $p$, such that the group $E_p(\mathbb{F}_p)$ is of order $N$. We show that $M_E(N)$ follows…

First we generalize the Thue-Morse sequence (the generalized Thue-Morse sequences) by a cyclic permutations and p-adic system, and consider the necessary-sufficient condition that it is non-periodic. Moreover if the generalized Thue-Morse…

Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process and edges exist between two points if and only if their distance is less than a fixed given…

In this paper, we define new generalized k-Mersenne numbers and give a formula of generalized Mersenne polynomials and further we study their properties. Moreover, we define Gaussian Mersenne numbers and obtain some identities like Binet…

It is known that if $x\in[0,1]$ is polynomial time random (i.e. no polynomial time computable martingale succeeds on the binary fractional expansion of $x$) then $x$ is normal in any integer base greater than one. We show that if $x$ is…

The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. Its mean and variance are known, but results for its median and mode are difficult to obtain, although a few cases have been solved and upper/lower…

In this paper, we prove that there are uncountable many real transcendental numbers, which are generated by digital pattern sequences. This generalizes the main theorem in Morton and Mourant, which states the existence of countable many…

The Generalized Poisson Distribution (GPD) was introduced by Consul and Jain (1973). However, as remarked by Consul (1989), "It is very difficult to prove by direct summation that the sum of all the probabilities is unity". We give a…

We calculate the level statistics by finding the eigenvalue spectrum for a variety of one-dimensional many-body models, namely the Heisenberg chain, the t-J model and the Hubbard model. In each case the generic behaviour is GOE, however at…

A new class of Poisson algebras, the class of {\em generalized Weyl Poisson algebras}, is introduced. It can be seen as Poisson algebra analogue of generalized Weyl algebras or as giving a Poisson structure to (certain) generalized Weyl…

S.Janson [Poset limits and exchangeable random posets, Combinatorica 31 (2011), 529--563] defined limits of finite posets in parallel to the emerging theory of limits of dense graphs. We prove that each poset limit can be represented as a…

A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…

A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…

We study Martin-L\"{o}f random (ML-random) points on computable probability measures on sample and parameter spaces (Bayes models). We consider variants of conditional randomness defined by ML-randomness on Bayes models and those of…

The strong recurrence is equivalent to the Riemann hypothesis. On the other hand, the generalized strong recurrence holds for any irrational number. In this paper, we show the generalized strong recurrence for all non-zero rational numbers.…

Let $\beta >1$ be an integer or generally a Pisot number. Put $T(x) = \{ \beta x \}$ on $[0,1]$ and let $S: [0,1]\to [0,1]$ be a piecewise linear transformation whose slopes have the form $\pm \beta^m$ with positive integers $m$. We give…

The Welschinger numbers, a kind of a real analog of the Gromov-Witten numbers which count the complex rational curves through a given generic collection of points, bound from below the number of real rational curves for any real generic…