Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Condensed Matter

arXiv:cond-mat/9411062 (cond-mat)
[Submitted on 16 Nov 1994]

Title:New tests of random numbers for simulations in physical systems

Authors:I. Vattulainen
View PDF
Abstract: The aim of this Thesis is to present five new tests for random numbers, which are widely used {\em e.g.} in computer simulations in physics applications. The first two tests, the cluster test and the autocorrelation test, are based on analogies to the two-dimensional Ising model. The next two, the random walk test and the $n$-block test, are based on studies of random walks, and the condition number test presented last uses some results of Gaussian distributed random matrices. Studies with several commonly used pseudorandom number generators reveal that the cluster test is particularly powerful in finding periodic correlations on bit level, and that the autocorrelation test, the random walk test, and the $n$-block test are very effective in detecting short-ranged correlations. The results of the condition number test are mostly inconclusive, however. By means of the tests presented in this work, two important results are found. First, we show quantitatively that the reason for erroneous results in some recent high precision Monte Carlo simulations for some commonly used pseudorandom number generators are the so called triple correlations in the sequences. Then, we show that the properties of such a sequence may be considerably improved, if only a certain portion of it is used.
Comments: Licentiate Thesis, LaTeX, 94 pages without figures. Uses this http URL, which is appended to the end of the paper. Complete (and compressed) PostScript file (including all figures) is available at this http URL or at this ftp URL lic_thesis.ps.Z (vattulai@convex.this http URL)
Subjects: Condensed Matter (cond-mat); High Energy Physics - Lattice (hep-lat); Cellular Automata and Lattice Gases (nlin.CG)
Report number: HU-TFT-IR-94-4
Cite as: arXiv:cond-mat/9411062
  (or arXiv:cond-mat/9411062v1 for this version)
  https://doi.org/10.48550/arXiv.cond-mat/9411062

Submission history

From: Ilpo Vattulainen [view email]
[v1] Wed, 16 Nov 1994 17:38:32 UTC (64 KB)
Full-text links:

Access Paper:

view license
Current browse context:
cond-mat
< prev   |   next >
new | recent | 1994-11

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
IArxiv Recommender (What is IArxiv?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)