相关论文: Maximal probabilities of convolution powers of dis…

We establish the unimodality and the asymptotic strong unimodality of the ordinary multinomials and give their smallest mode leading to the expression of the maximal probability of convolution powers of the discrete uniform distribution. We…

An algorithm is presented which, with optimal efficiency, solves the problem of uniform random generation of distribution functions for an n-valued random variable.

We give the distribution of $M_n$, the maximum of a sequence of $n$ observations from a moving average of order 1. Solutions are first given in terms of repeated integrals and then for the case where the underlying independent random…

Let $X_1,\ldots,X_n$ be independent identically distributed random vectors in $\mathbb{R}^d$. We consider upper bounds on $\max_x \mathbb{P}(a_1X_1+\cdots+a_nX_n=x)$ under various restrictions on $X_i$ and the weights $a_i$. When…

We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better…

Let $M_n$ be an $n$ by $n$ random matrix where each entry is +1 or -1 independently with probability 1/2. Our main result implies that the probability that $M_n$ is singular is at most $(1/\sqrt{2} + o(1))^n$, improving on the previous best…

We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…

A probability inequality is proved for n-fold convolutions of a smooth cumulative distribution function on (0,infinity)x...x(0,infinity), which is multivariate totally positive of order 2 (MTP2). This inequality is better than an inequality…

We prove a uniform generalized gaussian bound for the powers of a discrete convolution operator in one space dimension. Our bound is derived under the assumption that the Fourier transform of the coefficients of the convolution operator is…

We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…

We consider the maximum coding rate achievable by uniformly-random codes for the deletion channel. We prove an upper bound that's within 0.1 of the best known lower bounds for all values of the deletion probability $d,$ and much closer for…

In this paper we study the asymptotic behavior of the maximum magnitude of a complex random polynomial with i.i.d. uniformly distributed random roots on the unit circle. More specifically, let $\{n_k\}_{k=1}^{\infty}$ be an infinite…

We derive new explicit bounds for the total variation distance between two convolution products of $n$ probability distributions, one of which having identical convolution factors. Approximations by finite signed measures of arbitrary order…

Many upper bounds for the moduli of polynomial roots have been proposed but reportedly assessed on selected examples or restricted classes only. Regarding quality measured in terms of worst-case relative overestimation of the maximum…

A recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, states that the maximum of the permanent of a matrix whose rows are unit vectors in l_p is attained either for the identity matrix I or for a constant…

In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…

Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.

This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…

Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…

We prove polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution. This positively answers a question…