相关论文: Permutation statistics of products of random permu…

The well known Erdos-Turan law states that the logarithm of an order of a random permutation is asymptotically normally distributed. The aim of this work is to estimate convergence rate in this theorem and also to prove analogous result for…

The limitation of permutation tests is that they assume exchangeability. It is shown that in generalized linear models one can construct permutation tests from score statistics in particular cases. When under the null hypothesis the…

Different ways to describe a permutation, as a sequence of integers, or a product of Coxeter generators, or a tree, give different choices to define a simple permutation. We recollect few of them, define new types of simple permutations,…

This paper investigates local spectral statistics of singular values for many products of independent large rectangular matrices, sampled from the ensemble of truncated unitary matrices with the invariant Haar measure. Our main contribution…

The distribution of money is analysed in connection with the Boltzmann distribution of energy in the degenerate states of molecules. Plots of the population density of income distribution for various countries are well reproduced by a Gamma…

When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…

Various statistics on wreath products are defined via canonical words, "colored" right to left minima and "colored" descents. It is shown that refined counts with respect to these statistics have nice recurrence formulas of…

Let ${X_1,...,X_n}$ be i.i.d. random observations. Let $\mathbb{S}=\mathbb{L}+\mathbb{T}$ be a $U$-statistic of order $k\ge2$ where $\mathbb{L}$ is a linear statistic having asymptotic normal distribution, and $\mathbb{T}$ is a…

Given a physical quantum system described by a Hilbert H, for any bounded quantum observable (a bounded self-adjoint operator) T it is possible to define several ''hidden observable'' functions f:H->R associated to T and for any quantum…

Every observation may follow a distribution that is randomly selected in a class of distributions. It is called the distribution uncertainty. This is a fact acknowledged in some research fields such as financial risk measure. Thus, the…

Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are…

Consider a random permutation of $kn$ objects that permutes $n$ disjoint blocks of size $k$ and then permutes elements within each block. Normalizing its cycle lengths by $kn$ gives a random partition of unity, and we derive the limit law…

A permutation $\pi \in S_n$ is said to {\it avoid} a permutation $\sigma \in S_k$ whenever $\pi$ contains no subsequence with all of the same pairwise comparisons as $\sigma$. For any set $R$ of permutations, we write $S_n(R)$ to denote the…

Let $s(n)$ denote the number of ones in the binary expansion of a natural number $n\in\mathbb{N}$. For any $t\in\mathbb{N}$ and $d\in\mathbb{Z}$, let $\mu_t(d)$ denote the asymptotic density of the set of those natural numbers $n$ for which…

For a distribution $p:=\{p_k\}_{k=1}^\infty$ on the positive integers, there are two natural ways to construct a random permutation in $S_n$ or of $\mathbb{N}$ from IID samples from $p$--the $p$-biased construction and the $p$-shifted…

We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…

The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…

We introduce and study new refinements of inversion statistics for permutations, such as k-step inversions, (the number of inversions with fixed position differences) and non-inversion sums (the sum of the differences of positions of the…

Probability distributions can be read as simple expressions of information. Each continuous probability distribution describes how information changes with magnitude. Once one learns to read a probability distribution as a measurement scale…

In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent…