相关论文: Finite-sample frequency distributions originating …

We study the probability distribution of the ratio of consecutive level spacings for embedded one plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between…

Given a normalized Orlicz function $M$ we provide an easy formula for a distribution such that, if $X$ is a random variable distributed accordingly and $X_1,...,X_n$ are independent copies of $X$, then the expected value of the p-norm of…

Neural network (NN) ensembles can reduce large prediction variance of NN and improve prediction accuracy. For highly nonlinear problems with insufficient data set, the prediction accuracy of NN models becomes unstable, resulting in a…

Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…

In this paper, we study the probability distribution of the observable $s = (1/N)\sum_{i=N-N'+1}^N x_i$, with $1 \leq N' \leq N$ and $x_1<x_2<\cdots< x_N$ representing the ordered positions of $N$ particles in a $1d$ one-component plasma,…

Let P_{n,m} denote the graph taken uniformly at random from the set of all planar graphs on {1,2,..., n} with exactly m(n) edges. We use counting arguments to investigate the probability that P_{n,m} will contain given components and…

The random Fibonacci chain is a generalisation of the classical Fibonacci substitution and is defined as the rule mapping $0\mapsto 1$ and $1 \mapsto 01$ with probability $p$ and $1 \mapsto 10$ with probability $1-p$ for $0<p<1$ and where…

In this paper, a new mixture family of multivariate normal distributions, formed by mixing multivariate normal distribution and skewed distribution, is constructed. Some properties of this family, such as characteristic function, moment…

We show that the hypothesis of regularity of the conditional distribution of the empiric average of a finite sample of IID random variables, given all the sample "fluctuations", which appeared in our earlier manuscript |1] in the context of…

Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and…

Suppose X is a frequency vector that follows a central multiple hyper-geometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We show that the probability that X…

We consider products of independent random matrices with independent entries. The limit distribution of the expected empirical distribution of eigenvalues of such products is computed. Let $X^{(\nu)}_{jk},{}1\le j,r\le n$, $\nu=1,...,m$ be…

Let $M(n, k, p)$ denote the maximum probability of the event $X_1 = X_2 = \cdots = X_n=1$ under a $k$-wise independent distribution whose marginals are Bernoulli random variables with mean $p$. A long-standing question is to calculate $M(n,…

Let $\mu$ be a probability measure on $\mathbb{R}$ with cumulative distribution function $F$, $(x_{i})_{1}^{n}$ a large i.i.d. sample from $\mu$, and $F_{n}$ the associated empirical distribution function. The Glivenko-Cantelli theorem…

Conditional on the extended Riemann hypothesis, we show that with high probability, the characteristic polynomial of a random symmetric $\{\pm 1\}$-matrix is irreducible. This addresses a question raised by Eberhard in recent work. The main…

Given $f:\{-1, 1\}^n \rightarrow \{-1, 1\}$, define the \emph{spectral distribution} of $f$ to be the distribution on subsets of $[n]$ in which the set $S$ is sampled with probability $\widehat{f}(S)^2$. Then the Fourier Entropy-Influence…

In this paper, we characterize compatibility of distributions and probability measures on a measurable space. For a set of indices $\mathcal J$, we say that the tuples of probability measures $(Q_i)_{i\in \mathcal J} $ and distributions…

We consider a Zipf--Poisson ensemble in which $X_i\sim\poi(Ni^{-\alpha})$ for $\alpha>1$ and $N>0$ and integers $i\ge 1$. As $N\to\infty$ the first $n'(N)$ random variables have their proper order $X_1>X_2>...>X_{n'}$ relative to each…

It is shown that the fraction f of imaginary frequency instantaneous normal modes (INM) may be defined and calculated in a random energy model(REM) of liquids. The configurational entropy S and the averaged hopping rate among the states R…

We estimate the expected value of certain function $f:\{-1,1\}^{n}\to\mathbb{R}$. For example, with computer assistance, we show that if $\Delta$ is the Laplacian of the Cayley graph of…