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Algorithm for normal random numbers
1Instituto de Ciencia de Materiales de Aragón, Consejo Superior de Investigaciones Científicas, and Universidad de Zaragoza, 50009-Zaragoza, Spain.
Summary
This study introduces a fast, simple algorithm for generating normally distributed pseudorandom numbers. The method simulates energy exchange between molecules, proving effective for applications like Monte Carlo simulations.
Area of Science:
- Computational Physics
- Statistical Mechanics
- Numerical Methods
Background:
- Pseudorandom number generation is crucial for simulations.
- Existing methods like the Box-Muller algorithm can be computationally intensive.
- Efficient and simple algorithms are needed for complex modeling.
Purpose of the Study:
- To develop a novel, efficient algorithm for generating normally distributed pseudorandom numbers.
- To demonstrate the algorithm's theoretical underpinnings and practical performance.
- To offer a faster alternative to established pseudorandom number generation techniques.
Main Methods:
- Simulating N molecules exchanging energy via a stochastic rule.
- Proving system ergodicity and the emergence of a Maxwell-like distribution in the N-->infinity limit.
- Implementing the algorithm in a few lines of computer code.
Main Results:
- The algorithm generates normally distributed pseudorandom deviates.
- It is approximately ten times faster than the Box-Muller algorithm.
- The method successfully passed performance tests, including Monte Carlo simulation of a 2D Ising model.
Conclusions:
- The proposed algorithm provides a simple, fast, and effective method for generating normally distributed pseudorandom numbers.
- Its efficiency and ease of implementation make it suitable for various computational tasks.
- This approach offers a significant improvement over existing methods for pseudorandom number generation.