Related papers: Pseudorandom Number Generators and the Square Site…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
We present a Monte Carlo study of the bond and site directed (oriented) percolation models in $(d+1)$ dimensions on simple-cubic and body-centered-cubic lattices, with $2 \leq d \leq 7$. A dimensionless ratio is defined, and an analysis of…
The generation of pseudo-random discrete probability distributions is of paramount importance for a wide range of stochastic simulations spanning from Monte Carlo methods to the random sampling of quantum states for investigations in…
Machine learning (ML) frameworks rely heavily on pseudorandom number generators (PRNGs) for tasks such as data shuffling, weight initialization, dropout, and optimization. Yet, the statistical quality and reproducibility of these…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
Marsaglia proposed recently xorshift generators as a class of very fast, good-quality pseudorandom number generators. Subsequent analysis by Panneton and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing several…
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.…
We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond…
In the present article, numerical simulations have been performed to find the bond and site percolation thresholds on two-dimensional Gabriel graphs (GG) for Poisson point processes. GGs belong to the family of proximity graphs and are…
This paper has a practical aim. For a long time, implementations of pseudorandom number generators in standard libraries of programming languages had poor quality. The situation started to improve only recently. Up to now, a large number of…
We establish new correlation bounds and pseudorandom generators for a collection of computation models. These models are all natural generalizations of structured low-degree $F_2$-polynomials that we did not have correlation bounds for…
Monte Carlo event generators are in a modern terminology the digital twins of collider-based particle physics experiment. We give an introduction into the application of MC generators for particle physics, discuss their different components…
We study the natural question of constructing pseudorandom generators (PRGs) for low-degree polynomial threshold functions (PTFs). We give a PRG with seed-length log n/eps^{O(d)} fooling degree d PTFs with error at most eps. Previously, no…
The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more…
It is shown that superefficient Monte Carlo computations can be carried out by using chaotic dynamical systems as non-uniform random-number generators. Here superefficiency means that the expectation value of the square of the error…
Quantum Monte Carlo methods provide in principle an accurate treatment of the many-body problem of the ground and excited states of condensed systems. In practice, however, uncontrolled errors such as those arising from the fixed-node and…
We study the ability of Transformer models to learn sequences generated by Permuted Congruential Generators (PCGs), a widely used family of pseudo-random number generators (PRNGs). PCGs introduce substantial additional difficulty over…
The Pseudo-Random Number Generators (PRNGs) are key tools in Monte Carlo simulations. More recently, the MIXMAX PRNG has been included in ROOT and Class Library for High Energy Physics (CLHEP) software packages and claims to be a state of…
This paper studies the problem of discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator, particularly in the non-translational case. Two families of results are obtained. First, in a…