A practical overview of generating random numbers for large-scale parallel computing. It explains how to keep Monte Carlo simulations reproducible and efficient when using many processors.

The material surveys different parallel architectures and the challenges these machines pose, such as load balancing, asynchronous execution, and migrating tasks. It then focuses on pseudorandom streams used by simulation processes, not just hardware generators. You’ll see approaches for creating independent sequences, including the idea of a pseudorandom tree where new streams are launched as simulations branch. The text compares classic generator families and offers pragmatic options for long, nonoverlapping sequences that help reduce variance across replicas. It also introduces the spectral test as a way to measure uniformity and independence across multiple dimensions, and it discusses how to arrange constants to improve independence and reproducibility without sacrificing performance.

How to map random number streams to simulation processes or threads.

Different strategies for branching and migrating random streams across processors.

What the spectral test measures and how it guides generator selection.

Practical guidance on choosing additive constants to create independent, long sequences.

Ideal for readers of parallel computing and Monte Carlo methods who want a grounded, implementable approach to random number generation on large, evolving systems.

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