Related papers: The Riff-Shuffle Distribution is Unimodal

We present an extension of the famous Littlewood-Offord problem when Bernoulli distributions are replaced with discrete log-concave distributions. A variant of the Littlewood-Offord problem for arithmetic progressions, as well as an…

Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal…

A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…

In this article we study a small random perturbation of a linear recurrence equation. If all the roots of its corresponding characteristic equation have modulus strictly less than one, the random linear recurrence goes exponentially fast to…

The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the the classical de Moivre--Laplace normal approximation in order to give an estimate at the tail…

The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…

This article was written for the Logic in Computer Science column in the February 2015 issue of the Bulletin of the European Association for Theoretical Computer Science. The intended audience is general computer science audience. The…

Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal…

We study the approximation of arbitrary distributions $P$ on $d$-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback--Leibler-type functional. We show that such an approximation exists if…

We show that the likelihood function for a multinomial vector observed under arbitrary interval censoring constraints on the frequencies or their partial sums is completely log-concave by proving that the constrained sample spaces comprise…

In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…

In this paper, we investigate the small scale equidistribution properties of randomised sums of Laplacian eigenfunctions (i.e. random waves) on a compact manifold. We prove small scale expectation and variance results for random waves on…

A modification of Mott-Smith method for predicting the one-dimensional shock wave solution is presented. Mott-Smith distribution function is used to construct the system of moment equations to study the steady-state structure of shock wave…

We show explicitly that the broad histogram single-spin-flip random walk dynamics does not give correct microcanonical average even in one dimension. The dynamics violates detailed balance condition by an amount which decreases with system…

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

The distribution of reversible programs tends to a limit as their size increases. For problems with a Hamming distance fitness function the limiting distribution is binomial with an exponentially small chance (but non~zero) chance of…

We determine the probability distribution for the field inside a random uniform distribution of electric or magnetic dipoles. For parallel dipoles, simulations and an analytical derivation show that although the average contribution from…

We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the…

The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the…