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The generation of pseudo-random numbers is fundamental to computational simulations, impacting applications such as statistical modeling, Monte Carlo methods, and Markov Chain Monte Carlo (MCMC). A reliable pseudo-random number generator (PRNG) must demonstrate a long period, uniform distribution, statistical robustness, and efficient parallelization to support scalable simulations. However, ensuring independence among parallelized streams presents challenges, necessitating alternatives to conventional approaches like the Linear Congruential Generator (LCG). This chapter delves into the underlying principles, constraints, and advancements in PRNGs, with a particular focus on contemporary methods such as Multiple Recursive Generators (MRG) and Matrix Congruential Generators (MCG), alongside strategies for optimizing computational performance.

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Introduction

  • 章节

  • 发表日期：

    2025年

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  • Lih-Yuan Deng,
  • Nirman Kumar,
  • Henry Horng-Shing Lu,
  • Ching-Chi Yang

摘要

The generation of pseudo-random numbers is fundamental to computational simulations, impacting applications such as statistical modeling, Monte Carlo methods, and Markov Chain Monte Carlo (MCMC). A reliable pseudo-random number generator (PRNG) must demonstrate a long period, uniform distribution, statistical robustness, and efficient parallelization to support scalable simulations. However, ensuring independence among parallelized streams presents challenges, necessitating alternatives to conventional approaches like the Linear Congruential Generator (LCG). This chapter delves into the underlying principles, constraints, and advancements in PRNGs, with a particular focus on contemporary methods such as Multiple Recursive Generators (MRG) and Matrix Congruential Generators (MCG), alongside strategies for optimizing computational performance.