Related papers: On testing pseudorandom generators via statistical…

This work considers the deployment of pseudo-random number generators (PRNGs) on graphics processing units (GPUs), developing an approach based on the xorgens generator to rapidly produce pseudo-random numbers of high statistical quality.…

Let $\mathbf{X}_1,...,\mathbf{X}_n$ be a random sample from a $p$-dimensional population distribution. Assume that $c_1n^{\alpha}\leq p\leq c_2n^{\alpha}$ for some positive constants $c_1,c_2$ and $\alpha$. In this paper we introduce a new…

When we want to simulate the realization of a symmetric simple random walk on $\mathbb Z^d$, we use $(2d)$-side fair dice to decide to which neighbor it jumps at each step if $d\geq 2$ or we simply use a fair coin when $d=1$. Assume that…

Two-sample hypothesis testing for large graphs is popular in cognitive science, probabilistic machine learning and artificial intelligence. While numerous methods have been proposed in the literature to address this problem, less attention…

We obtain non-uniform Berry-Esseen type estimates for several classes of weakly dependent sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or expanding…

We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact…

A technique for controlling errors in the functioning of nodes for the formation of $q$-valued pseudo-random sequences (PRS) operating under both random errors and errors generated through intentional attack by an attacker is provided, in…

In this paper, we develop a simple approach for testing multiple statistical hypotheses based on the observations of a number of probability ratios enumerated consecutively with respect to the index of hypotheses. Explicit and tight bounds…

We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…

This paper is concerned with the limit theory of the extreme order statistics derived from random walks. We establish the joint convergence of the order statistics near the minimum of a random walk in terms of the Feller chains. Detailed…

Security of information transmitted through the Internet, against passive or active attacks is an international concern. The use of a chaos-based pseudo-random bit sequence to make it unrecognizable by an intruder, is a field of research in…

Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay…

Random numbers are commonly used in many different fields, ranging from simulations in fundamental science to security applications. In some critical cases, as Bell's tests and cryptography, the random numbers are required to be both secure…

We explore the asymptotic distributions of sequences of integer-valued additive functions defined on the symmetric group endowed with the Ewens probability measure as the order of the group increases. Applying the method of factorial…

The paper discusses a statistical problem related to testing for differences between two sparse networks with community structures. The community-wise edge probability matrices have entries of order $O(n^{-1}/\log n)$, where $n$ represents…

We study the equivalence testing problem where the goal is to determine if the given two unknown distributions on $[n]$ are equal or $\epsilon$-far in the total variation distance in the conditional sampling model (CFGM, SICOMP16; CRS,…

Minimum Bayes-risk (MBR) decoding has recently gained renewed attention in text generation. MBR decoding considers texts sampled from a model as pseudo-references and selects the text with the highest similarity to the others. Therefore,…

We study human dynamics by analyzing Linux history files. The goodness-of-fit test shows that most of the collected datasets belong to the universality class suggested in the literature by a variable-length queueing process based on…

We prove that the sum of $t$ boolean-valued random variables sampled by a random walk on a regular expander converges in total variation distance to a discrete normal distribution at a rate of $O(\lambda/t^{1/2-o(1)})$, where $\lambda$ is…

Biometric recognition is used across a variety of applications from cyber security to border security. Recent research has focused on ensuring biometric performance (false negatives and false positives) is fair across demographic groups.…