# Pseudo-random-number generators and the square site percolation threshold.

@article{Lee2008PseudorandomnumberGA, title={Pseudo-random-number generators and the square site percolation threshold.}, author={Michael J. Lee}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2008}, volume={78 3 Pt 1}, pages={ 031131 } }

Selected pseudo-random-number generators are applied to a Monte Carlo study of the two-dimensional square-lattice site percolation model. A generator suitable for high precision calculations is identified from an application specific test of randomness. After extended computation and analysis, an ostensibly reliable value of p_{c}=0.59274598(4) is obtained for the percolation threshold.

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## References

SHOWING 1-10 OF 12 REFERENCES

### Introduction To Percolation Theory

- Physics
- 1985

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in…

### Applications of percolation theory

- Materials Science
- 1994

Connectivity as the Essential Physics of Disordered Systems Elements of Percolation Theory Characterization of Porous Media Earthquakes, and Fracture and Fault in Patterns in Heterogeneous Rock…

### Applications of number theory to numerical analysis

- Mathematics
- 1981

1. Algebraic Number Fields and Rational Approximation.- 1.1. The units of algebraic number fields.- 1.2. The simultaneous Biophantine approximation of an integral basis.- 1.3. The real eyelotomie…

### The Art in Computer Programming

- Art
- 2001

Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on.

### Random Struct

- Algorithms 26, 392
- 2005

### Laboratory for Scientific Computing

- University of Michigan, Report No. 88-4, Footnote 26
- 1988

### ANZIAM Journal 48

- C188
- 2007