Below, we give an overview of our research and publications on theoretical, empirical and computational aspects of random number generation and related topics (the named publications are available in bibtex format). Selected empirical results and documentations are also available in our pLab report series.

Of course, this list of publications is not up to date - we prefer research to administration. For the newest results, please contact us personally.

THEORETICAL RESULTS

Entacher, K.: Generalized Haar function systems in the theory of uniform distributions of sequences modulo one. PhD thesis, University of Salzburg, 1995. Karl Entacher will send you his thesis in postscript on request.

Entacher, K.: Numerical integration with generalized Haar function systems. In Hellekalek, P. and Larcher, G. and Zinterhof, P., editor(s), Proceedings of the 1st Salzburg Minisymposium on Pseudorandom Number Generation and Quasi-Monte Carlo Methods, Salzburg, Nov 18, 1994, volume ACPC/TR 95-4 of Technical Report Series, pp. 25--41. ACPC -- Austrian Center for Parallel Computation, University of Vienna, Austria, 1995. Abstract available.

Entacher, K.: Generalized Haar function systems, digital nets and quasi-Monte Carlo integration. In H.H. Szu, editor(s), Wavelet Applications III of Proc. SPIE 2762. , 1996. Abstract available.

Entacher, K.: Quasi-Monte Carlo methods for numerical integration of multivariate Haar series. BIT, 37: (4) 846--861, 1997.

Entacher, K.: Quasi-Monte Carlo methods for numerical integration of multivariate Haar series II. BIT, 38: (2) 284--292, 1998.

Entacher, K.: A collection of selected pseudorandom number generators with linear structures, number 97-1. ACPC -- Austrian Center for Parallel Computation, University of Vienna, Austria, 1997. Abstract available.

Entacher, K.: Bad subsequences of well-known linear congruential pseudorandom number generators. ACM Transactions on Modeling and Computer Simulation, 7: (1) 61--70, 1998.

Entacher, K.: Parallel Streams of Linear Random Numbers in the Spectral Test. ACM Transactions on Modeling and Computer Simulation, :, 1999. To appear.

Entacher, K.: On the Cray-System Random Number Generator. 1999. SIMULATION to appear.

Entacher, K. and Hellekalek, P. and L'Ecuyer, P.: Quasi-Monte Carlo Integration with Linear Congruential Generators. 1999. To appear in the conference proceedings of Monte Carlo and Quasi-Monte Carlo Methods 1998, Springer-Verlag.

Hellekalek, P.: General discrepancy estimates: the Walsh function system. Acta Arith., 67: 209--218, 1994.

Hellekalek, P.: General discrepancy estimates II: the Haar function system. Acta Arith., 67: 313--322, 1994.

Hellekalek, P.: General discrepancy estimates III: the Erdös-Turán-Koksma inequality for the Haar function system. Monatsh. Math., 120: 25--45, 1995.

Hellekalek, P.: Study of algorithms for primitive polynomials. Report D5H-1, CEI-PACT Project, WP5.1.2.1.2, Research Institute for Software Technology, University of Salzburg, Austria, 1994. Abstract available.

Hellekalek, P.: Inversive pseudorandom number generators: concepts, results, and links. In Alexopoulos, C. and Kang, K. and Lilegdon, W.R. and Goldsman, D., editor(s), Proceedings of the 1995 Winter Simulation Conference, pp. 255--262. , 1995. Abstract available.

Hellekalek, P. and Entacher, K.: Tables of IMP-polynomials. Report D5H-4, CEI-PACT Project, WP5.1.2.1.2, Research Institute for Software Technology, University of Salzburg, Austria, 1995. Abstract available.

Hellekalek, P. and Niederreiter, H.: The Weighted Spectral Test: Diaphony. ACM Transactions on Modeling and Computer Simulation, 8: (1) , 1998.

Hellekalek, P. and Leeb, H.: Dyadic diaphony. Acta Arith., 80: 187-196, 1997. Abstract available.

ellekalek, P.: On correlation analysis of pseudorandom numbers. In Niederreiter, H. and Hellekalek, P. and Larcher, G. and Zinterhof, P., editor(s), Proceedings of the Second International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Salzburg, July 9--12, 1996 of Lecture Notes in Statistics. Springer-Verlag, New York, .

Hellekalek, P.: Good random number generators are (not so) easy to find. In Troch, I. and Breitenecker, F., editor(s), Proc. Second IMACS Symposium on Mathematical Modelling, Vienna. ARGESIM-Reports, ISBN 3-901608-11-7, .

Hellekalek, P.: On the assessment of random and quasi-random point sets. In Hellekalek, P. and Larcher, G., editor(s), Pseudo and Quasi-Random Point Sets of Lecture Notes in Statistics. Springer-Verlag, New York, 1998.

Leeb, H.: Random Numbers for Computer Simulation. Master's thesis, University of Salzburg, 1995. Abstract available.

Leeb, H.: A weak law for diaphony. RIST++ 13, Research Institute for Software Technology, University of Salzburg, 1996. Abstract available.

Leeb, H.: The asymptotic distribution of diaphony in one dimension. G-96-52, GERAD - Ecole des Hautes Etudes Commerciales, Montreal, 1996. Abstract available.

Leeb, H.: Weak limits for diaphony. Lecture Notes in Stat., 1997. to appear. Abstract available.

Wegenkittl, S.: Empirical Testing of Pseudorandom Number Generators. Master's thesis, Universität Salzburg, Österreich, 1995. HTML version: http://random.mat.sbg.ac.at/~ste/dipl..

Wegenkittl, S.: Are there hyperbola in the scatter plots of inversive congruential pseudorandom numbers?. J. Computational And Applied Mathematics, 95: (1-2) 117--125, 1998.

Wegenkittl, S.: Generalized Phi-Divergence and Frequency Analysis in Markov Chains. PhD thesis, Universität Salzburg, Österreich, 1998. HTML version: http://random.mat.sbg.ac.at/~ste/diss..

Wegenkittl, S.: A generalized -divergence for asymptotically multivariate normal models.
1999. Submitted for publication..

Wegenkittl, S.: Gambling Tests for Pseudorandom Number Generators.
1999. To appear in Mathematics and Computers in Simulation..

Weingartner, A.: Nonlinear congruential pseudorandom number generators. Master's thesis, University of Salzburg, 1994. Abstract available.

Schaber, K.: Digital inversive congruential generators. Master's thesis, Institut für Mathematik, Universität Salzburg, Austria, 1997. Thesis in postscript available on request.

EMPIRICAL RESULTS

Entacher, K.: Selected random number generators in run tests. Preprint, Mathematics Institute, University of Salzburg.

Entacher, K. and Leeb, H.: Inversive pseudorandom number generators: empirical results. In Proceedings of the Conference Parallel Numerics 95, Sorrento, Italy, September 27--29, 1995. , 1995. Abstract available.

Hellekalek, P. and Mayer, M. and Weingartner, A.: Implementation of algorithms for IMP-polynomials. Report D5H-2, CEI-PACT Project, WP5.1.2.1.2, Research Institute for Software Technology, University of Salzburg, Austria, 1994. Abstract available.

Leeb, H.: On the digit test. In Hellekalek, P. and Larcher, G. and Zinterhof, P., editor(s), Proceedings of the 1st Salzburg Minisymposium on Pseudorandom Number Generation and Quasi-Monte Carlo Methods, Salzburg, Nov 18, 1994, volume ACPC/TR 95-4 of Technical Report Series, pp. 109--121. ACPC -- Austrian Center for Parallel Computation, University of Vienna, Austria, 1995. Abstract available.

Leeb, H. and Wegenkittl, S.: Inversive and linear congruential pseudorandom number generators in selected empirical tests. ACM Transactions on Modeling and Computer Simulation, 7: (2) , 1997. Abstract available.

Eichenauer-Herrmann, J. and Herrmann, E. and Wegenkittl, S.: A survey of quadratic and inversive congruential pseudorandom numbers. In Niederreiter, H. and Hellekalek, P. and Larcher, G. and Zinterhof, P., editor(s), Monte Carlo and Quasi-Monte Carlo Methods 1996, number 127 of Lecture Notes in Statistics, pp. 66--97. Springer, New York, 1997.

L'Ecuyer, P. and Simard, R. and Wegenkittl, S.: Sparse Serial Tests of Uniformity for Random Number Generators. 1998. Submitted for publication.

Wegenkittl, S.: On Empirical Testing of Pseudorandom Number Generators. In De Pietro,G. and Giordano, A. and Vajtersic, M. and Zinterhof, P., editor(s), Proceedings of the international workshop Parallel Numerics '95. CEI-PACT Project, WP5.1.2.1.2. , 1995.

Entacher, K. and Uhl, A. and Wegenkittl, S.: Analyzing Streams of Pseudorandom Numbers for Parallel Monte Carlo Integration. In Wyrzykowski, R. and Piech, H. and Vajtersic, M. and Zinterhof, P., editor(s), Proceedings of the international Workshop Parallel Numerics' 97, pp. 59--71. , Zakopane, Poland, 1997.

Entacher, K. and Uhl, A. and Wegenkittl, S.: Linear and Inversive Pseudorandom Numbers for Parallel and Distributed Simulation. In Twelfth Workshop on Parallel and Distributed Simultation PADS'98, pp. 90--97. IEEE Computer Society, Los Alamitos, California, Banff, Alberta, Canada, 1998.

Entacher, K. and Uhl, A. and Wegenkittl, S.: Parallel Random Number Generation: Long-Range Correlations Among Multiple Processors. In Zinterhof, P. and Vajtersic, M. and Uhl, A., editor(s), Parallel Computation. Proceedings of the 4th International Conference of the ACPC ( ACPC99) of Lecture Notes in Computer Science, pp. 107--116. Springer-Verlag, 1999.

L'Ecuyer, P. and Hellekalek, P.: Testing random number generators. In Hellekalek, P. and Larcher, G., editor(s), Random and Quasi-Random Point Sets of Lecture Notes in Statistics, pp. 223-265. Springer-Verlag, New York, .

Entacher, K. and Hellekalek, P. and L'Ecuyer, P.: Quasi-Monte Carlo node sets from linear congruential generators. In Niederreiter, H. and Spanier, J., editor(s), Monte Carlo and Quasi-Monte Carlo Methods 1998 of Springer Lectures Notes in Computational Science end Engineering. Springer-Verlag, New York, 2000.

Hellekalek, P.: Don't trust parallel Monte Carlo!. In Twelfth Workshop on Parallel and Distributed Simulation, Pads'98, May 26-29, 1998, Banff, Alberta, Canada, pp. 82-89. IEEE Computer Society, Los Alamitos, California, .

SOFTWARE
Otmar Lendl implemented portable, high-performance ANSI-C implementations of the linear congruential, inversive congruential and explicit inversive congruential random number generators (LCG, ICG and EICG, respectively). The source-code is available in tar-ed or zip-ed format.

pLab is an object oriented system for generating and testing random numbers designed by Hannes Leeb under the supervision of Peter Hellekalek. It was implemented in C++ by Thomas Auer, Hannes Leeb and Otmar Lendl, in Mathematica by Karl Entacher, and in Smalltalk 80 by Hannes Leeb. We use it to for various statistical tests, discrepancy computations and scatter plots. You can download it to test your generator.
Important notice! We are sorry, but we cannot support pLab any longer. For this reason, you will have to cope with problems yourself. For more information on pLab, see

Leeb, H.: pLab -- a system for generating and testing random numbers. Report No. 3, pLab -- reports, University of Salzburg, 1997. Abstract and compressed postscript file available .

Leeb, H. and Lendl, O.: pLab -- Library reference, Version 1.0. Report No. 4, pLab -- reports, University of Salzburg, 1997. Abstract and compressed postscript file available .

Leeb, H.: pLab -- a system for testing random numbers. In Vajtersic, M. and Zinterhof, P., editor(s), Proceedings of the International Workshop Parallel Numerics '94, Smolenice, Sept. 19--21, pp. 89--99. Slovak Academy of Sciences, Institute for Informatics, Slovakia, 1994. Abstract available.

PLAB - REPORT SERIES
The aim of this report series is the fast distribution of recent results of the pLab research group. Some of these postscript documents (rep. 1,2,6) are very large (5 MB), download the compressed versions!

Wegenkittl, S.: The pLab Picturebook: Load Tests and Ultimate Load Tests, Part I. Report No. 1, pLab -- reports, University of Salzburg, 1997. Abstract and compressed postscript file available.

Entacher, K. and Wegenkittl, Stefan: The pLab Picturebook: Load Tests and Ultimate Load Tests, Part II: Subsequences. Report No. 2, pLab -- reports, University of Salzburg, 1997. Abstract and compressed postscript file available .

Leeb, H.: pLab -- a system for generating and testing random numbers. Report No. 3, pLab -- reports, University of Salzburg, 1997. Abstract and compressed postscript file available.

Leeb, H. and Lendl, O.: pLab -- Library reference, Version 1.0. Report No. 4, pLab -- reports, University of Salzburg, 1997. Abstract and compressed postscript file available.

Entacher, K.: The pLab Picturebook Part III: Bad Subsequences of LCGs -- The Results. Report No. 6, pLab -- reports, University of Salzburg, 1997. Abstract and compressed postscript file available. This report must be seen in connection with our collection of selected pseudorandom number generators with linear structures.

Wegenkittl, S.: The pLab Picturebook: Load Tests and Ultimate Load Tests, Addendum. Report No. 7, pLab -- reports, University of Salzburg, 1997. Abstract available.

Wegenkittl, S.: The pLab Picturebook: Load Tests for the SG100 Security Generator. Report No. 8, pLab -- reports, University of Salzburg, 1997. Abstract available.

Hellekalek, P.: On the assessment of random and quasi-random point sets. In Hellekalek, P. and Larcher, G., editor(s), Pseudo and Quasi-Random Point Sets of Lecture Notes in Statistics. Springer-Verlag, New York, 1998.

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