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We study the Euler-Frobenius numbers, a generalization of the Eulerian numbers, and the probability distribution obtained by normalizing them. This distribution can be obtained by rounding a sum of independent uniform random variables; this…
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…
We consider uniform random permutations in proper substitution-closed classes and study their limiting behavior in the sense of permutons. The limit depends on the generating series of the simple permutations in the class. Under a mild…
In this paper, we propose to obtain the skewed version of a unimodal symmetric density using a skewing mechanism that is not based on a cumulative distribution function. Then we disturb the unimodality of the resulting skewed density. In…
A complete characterization of the asymptotic singularity probability of random circulant Bernoulli matrices is given for all values of the probability parameter.
In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall…
For a wide class of sequences of integer domains $\mathcal{D}_n\subset\mathbb{N}^d$, $n\in\mathbb{N}$, we prove distributional limit theorems for $F(X_1^{(n)},\ldots,X_d^{(n)})$, where $F$ is a multivariate multiplicative function and…
We compute an asymptotic estimate for odd balanced unimodal sequences for ranks congruent to $a \pmod{c}$ for $c\neq 1$ odd. We find the interesting result that the odd balanced unimodal sequences are asymptotically related to the…
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…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
We consider a generalization of the discrete memoryless channel, in which the channel probability distribution is replaced by a uniform distribution over clouds of channel output sequences. For a random ensemble of such channels, we derive…
We establish an alternative, ``perpendicular" collection of generating functions for the coefficients of Gaussian polynomials, $\begin{bmatrix}N+m\\m\end{bmatrix}_q$. We provide a general characterization of these perpendicular generating…
The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided…
We compute the limit distribution of partial transposes (when both the number and the size of blocks tends to infinity) for a large class of ensembles of unitarily invariant random matrices. Furthermore, it is shown the asymptotic freeness…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
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…
This work examines various statistical distributions in connection with random Vandermonde matrices and their extension to $d$--dimensional phase distributions. Upper and lower bound asymptotics for the maximum singular value are found to…
There is a natural pluripotential-theoretic extremal function V_{K,Q} associated to a closed subset K of C^m and a real-valued, continuous function Q on K. We define random polynomials H_n whose coefficients with respect to a related…
We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.
This paper presents a study of power series distributions (PSD) with prescribed covariance characteristics. Such distributions constitute a fundamental class in probability theory and mathematical statistics, as they generalize a wide range…