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This paper presents theory for Normalized Random Measures (NRMs), Normalized Generalized Gammas (NGGs), a particular kind of NRM, and Dependent Hierarchical NRMs which allow networks of dependent NRMs to be analysed. These have been used,…

Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called…

Quantum random number generator (QRNG) can produce true randomness by utilizing the inherent probabilistic nature of quantum mechanics. Recently, the spontaneous-emission quantum phase noise of the laser has been widely deployed for QRNG,…

Random numbers are central to various applications such as secure communications, quantum key distribution theory (QKD), statistics, and other tasks. One of today's most popular generators is quantum random numbers (QRNGs). The inherent…

In this article we present the prototype of a framework capable of producing, with linear complexity, uniformly random XML documents with respect to a given RELAX NG grammar. The generation relies on powerful combinatorial methods together…

We consider the problem of enumeration of primitive TSRs of order n over any finite field. Here we prove the existence of primitive TSRs of order two over binary field extensions. Moreover we give a general search algorithm for primitive…

We analyze and partially solve system of recurrences that can be derived from the properties of martingale orthogonal polynomials that characterize quadratic harnesses (QH). We also specify conditions for the existence of moments of one…

We present an intriguing discovery related to Random Fourier Features: in Gaussian kernel approximation, replacing the random Gaussian matrix by a properly scaled random orthogonal matrix significantly decreases kernel approximation error.…

This paper targets to search so-called \emph{good} generators by doing a brief survey over the generators developed in the history of pseudo-random number generators (PRNGs), verify their claims and rank them based on strong empirical tests…

Stochastic simulations are often sensitive to the source of randomness that character-izes the statistical quality of their results. Consequently, we need highly reliable Random Number Generators (RNGs) to feed such applications. Recent…

This project develops a pseudo-random number generator (PRNG) using the logistic map, implemented in Verilog HDL on an FPGA and processes its output through a Central Limit Theorem (CLT) function to achieve a Gaussian distribution. The…

We apply the real space Renormalisation Group (RNG) technique to a variety of one-dimensional Ising chains. We begin by recapitulating the work of Nauenberg for an ordered Ising chain, namely the decimation approach. We extend this work to…

Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…

A common approach to analyze count time series is to fit models based on random sum operators. As an alternative, this paper introduces time series models based on a random multiplication operator, which is simply the multiplication of a…

Emergence of stochastic simulations as an extensively used computational tool for scientific purposes intensified the need for more accurate ways of generating sufficiently long sequences of uncorrelated random numbers. Even though several…

Random number generators (RNG) based on quantum mechanics are captivating due to their security and unpredictability compared to conventional generators, such as pseudo-random number generators and hardware-random number generators. This…

In this paper, we propose primitive rateless (PR) codes. A PR code is characterized by the message length and a primitive polynomial over $\mathbf{GF}(2)$, which can generate a potentially limitless number of coded symbols. We show that…

Random graph generation is an important tool for studying large complex networks. Despite abundance of random graph models, constructing models with application-driven constraints is poorly understood. In order to advance state-of-the-art…

We prove new results on the polarizing random walk framework introduced in recent works of Chattopadhyay {et al.} [CHHL19,CHLT19] that exploit $L_1$ Fourier tail bounds for classes of Boolean functions to construct pseudorandom generators…

Random numbers are an essential resource to many applications, including cryptography and Monte Carlo simulations. Quantum random number generators (QRNGs) represent the ultimate source of randomness, as the numbers are obtained by sampling…