Related papers: Random weighted averages, partition structures and…
We prove a long-standing conjecture which characterises the Ewens-Pitman two-parameter family of exchangeable random partitions, plus a short list of limit and exceptional cases, by the following property: for each $n = 2,3, >...$, if one…
Pitman(2003)(and subsequently Gnedin and Pitman (2006) showed that a large class of random partitions of the integers derived from a stable subordinator of index $\alpha\in(0,1)$ have infinite Gibbs (product) structure as a characterizing…
Let $X_1,\ldots,X_N$ be i.i.d.\ random variables distributed like $X$. Suppose that the first $k \geq 3$ moments $\{ \mathbb{E}[X^j] : j = 1,\ldots,k\}$ of $X$ agree with that of the standard Gaussian distribution, that…
Random Quantum States are presently of interest in the fields of quantum information theory and quantum chaos. Moreover, a detailed study of their properties can shed light on some foundational issues of the quantum statistical mechanics…
Recently, a new formalism describing the anomalous diffusion processes, based on the Onsager-Machlup fluctuation theory, has been suggested \cite{Smain, Spub}. We study particles performing this new type of motion, under the action of…
The paper deals with three generalized dependent setups arising from a sequence of Bernoulli trials. Various distributional properties, such as probability generating function, probability mass function and moments are discussed for these…
Commonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of the common continuous distributions. His…
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising multivariate Hermite orthogonal polynomials in dependent Gaussian random variables. The second-moment properties of Hermite polynomials reveal a weakly…
The purpose of this paper is to prove directly, by an elementary method, the Poisson probability law. This proof is offered as an alternative to the more usual derivation from binomial distribution in the limit of small probabilities. The…
In spite of its title, the book mostly treats probability theory: the law of large numbers (regarded as a principle); formal definition of a random variable and law of distribution; the misnamed Cauchy distribution; functions now named…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
A theorem of Meinardus provides asymptotics of the number of weighted partitions under certain assumptions on associated ordinary and Dirichlet generating functions. The ordinary generating functions are closely related to Euler's…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
An important line of research is the investigation of the laws of random variables known as Dirichlet means as discussed in Cifarelli and Regazzini(1990). However there is not much information on inter-relationships between different…
The Poisson-Kingman distributions, $\mathrm{PK}(\rho)$, on the infinite simplex, can be constructed from a Poisson point process having intensity density $\rho$ or by taking the ranked jumps up till a specified time of a subordinator with…
According to the Wagstaff heuristic, the probability that a Mersenne number $M_p = 2^p-1$ is prime mainly depends on the size of the exponent $p$. We investigate whether the secondary arithmetic structure in $p-1$ is linked to noticeable…
The paper is concerned with the asymptotic analysis of a family of Boltzmann (multiplicative) distributions over the set $\check{\varLambda}^{q}$ of strict integer partitions (i.e., with unequal parts) into perfect $q$-th powers. A…
We consider ensembles of random polynomials of the form $p(z)=\sum_{j = 1}^N a_j P_j$ where $\{a_j\}$ are independent complex normal random variables and where $\{P_j\}$ are the orthonormal polynomials on the boundary of a bounded simply…
Given uniform probability on words of length M=Np+k, from an alphabet of size p, consider the probability that a word (i) contains a subsequence of letters (p, p-1,...,1) in that order and (ii) that the maximal length of the disjoint union…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…