Physical models as tests of randomness.
Physical models as tests of randomness.
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DOI：
10.1103/physreve.52.3205
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发表时间：
1995-09
期刊：
影响因子：
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通讯作者：
I. Vattulainen;T. Ala‐Nissila;K. Kankaala
中科院分区：
文献类型：
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作者：
I. Vattulainen;T. Ala‐Nissila;K. Kankaala
提出并详细分析了一种基于物理模型的随机数序列测试平台。前两个检验，即簇检验和自相关检验，完全基于二维伊辛模型的已知性质。另外两个，随机游走检验和n{块检验，都是基于格上的随机游走。我们已经将这些测试应用于一些常用的伪随机数生成器。簇检验特别适合于检测比特水平上的周期相关性，而自相关、随机游走和n块检验非常适合于研究随机数序列中的弱相关性。基于测试结果，我们论证了最近高精度蒙特卡罗模拟中误差背后的原因，并讨论了如何避免这些误差。
We present and analyze in detail a test bench for random number sequences based on the use of physical models. The rst two tests, namely the cluster test and the autocorrelation test, are based on exactly known properties of the two{dimensional Ising model. The other two, the random walk test and the n{block test, are based on random walks on lattices. We have applied these tests to a number of commonly used pseudorandom number generators. The cluster test is shown to be particularly eecient in detecting periodic correlations on bit level, while the autocorrelation, the random walk, and the n{block tests are very well suited for studies of weak correlations in random number sequences. Based on the test results, we demonstrate the reasons behind errors in recent high precision Monte Carlo simulations, and discuss how these could be avoided.