Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New tests of random numbers for simulations in physical systems   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.

10
The categories of this paper are: q-bio
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs