Algorithm for normal random numbers

TL;DR

This paper introduces a simple, fast algorithm for generating normally distributed pseudo random numbers based on a stochastic energy exchange model, proven to produce Maxwell-like distributions and validated through performance tests.

Contribution

It presents a novel, minimalistic algorithm for normal random number generation that is faster and simpler than existing methods like Box-Muller.

Findings

Algorithm is approximately ten times faster than Box-Muller.

It produces Maxwell-like distributions as N tends to infinity.

The method successfully passes various performance tests, including Monte Carlo simulations.

Abstract

We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and that a Maxwell like distribution that may be used as a source of normally distributed random deviates follows when N tends to infinity. The algorithm passes various performance tests, including Monte Carlo simulation of a finite 2D Ising model using Wolff's algorithm. It only requires four simple lines of computer code, and is approximately ten times faster than the Box-Muller algorithm.