Related papers: Random weighted averages, partition structures and…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
We probabilistically analyze the performance of the arithmetic coding algorithm under a probability model for binary data in which a message is received by a coder from a source emitting independent equally distributed bits, with 1…
An important functional of Poisson random measure is the negative binomial process (NBP). We use NBP to introduce a generalized Poisson-Kingman distribution and its corresponding random discrete probability measure. This random discrete…
In earlier work generalizing a 1977 theorem of Alladi, the authors proved a partition-theoretic formula to compute arithmetic densities of certain subsets of the positive integers $\mathbb N$ as limiting values of $q$-series as $q\to \zeta$…
We study the distribution of the least singular value associated to an ensemble of sparse random matrices. Our motivating example is the ensemble of $N\times N$ matrices whose entries are chosen independently from a Bernoulli distribution…
We consider the space $\mathcal{P}(X)$ of probability measures on arbitrary Radon space $X$ endowed with a transportation cost $J(\mu, \nu)$ generated by a nonnegative continuous cost function. For a probability distribution on…
The statistical problem of the distribution of $s$ quanta of equal energy $\epsilon_0$ and total energy $E$ among $N$ distinguishable particles is resolved using the conventional theory based on Boltzmann's principle of equal probabilities…
The asymptotic distribution of the likelihood-ratio statistic for testing parameters on the boundary is well known to be a chi-squared mixture. The mixture weights have been shown to correspond to the intrinsic volumes of an associated…
The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the…
Gibbs-type exchangeable random partitions, which is a class of multiplicative measures on the set of positive integer partitions, appear in various contexts, including Bayesian statistics, random combinatorial structures, and stochastic…
We consider Bernoulli distributions and their regularizations, which are measures on the $p$-adic integers $\mathbb{Z}_p$. It is well known that their Mellin transform can be used to define $p$-adic $L$-functions. We show that for $p>2$ one…
Let $\{X_i\}$ be a sequence of independent identically distributed random variables with an intermediate regularly varying (IR) right tail $\bar{F}$. Let $(N, C_1, ..., C_N)$ be a nonnegative random vector independent of the $\{X_i\}$ with…
In this paper, we characterize the multivariate uniform probability distribution of the first and second kinds in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Their bivariate distributions and related properties,…
Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…
Let $a_n$ be the random increasing sequence of natural numbers which takes each value independently with probability $n^{-a}$, $0 < a < 1/2$, and let $p(n) = n^{1+\epsilon}$, $0 < \epsilon < 1$. We prove that, almost surely, for every…
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter…
The norm of an integer partition is defined as the product of its parts. This statistic was recently introduced by Schneider in connection to partition zeta functions. In this note, we use the method of moments to study the distribution of…
The classical Mertens' formula states that $ \prod_{p\le N}\big(1-\frac1p)^{-1}\sim e^\gamma\log N, $ where the product is over all primes $p$ less than or equal to $N$, and $\gamma$ is the Euler-Mascheroni constant. By the Euler product…
The paper is concerned with constructing pairwise dependence between $m$ random density functions each of which is modeled as a mixture of Dirichlet process model. The key to this is how to create dependencies between random Dirichlet…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…