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A fast random number generator for stochastic simulations. (English) Zbl 1197.65009
Summary: A discrete random number (DRN) generator for stochastic differential equations is proposed. The generator has exactly 8 states and thus 10 DRN’s can be obtained from a single 32-bit random variable. This is advantageous when large numbers of DRN’s are needed, as for example in fluctuating lattice-Boltzmann models. The moments of the discrete distribution match those of a Gaussian distribution (zero mean and unit variance) up to 5th order. Numerical tests show that satisfactory statistical properties can be obtained with several 32-bit pseudo random number (PRN) generators.

MSC:
65C10 Random number generation in numerical analysis
Software:
Diehard; dieharder
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[1] Dünweg, B.; Paul, W., Int. J. mod. phys. C, 2, 817, (1991)
[2] Öttinger, H.C., Stochastic processes in polymeric fluids, (1996), Springer-Verlag
[3] Kloeden, P.E.; Platen, E., Numerical solution of stochastic differential equations, Applications of mathematics, vol. 23, (1993), Springer · Zbl 0701.60054
[4] Ladd, A.J.C., Phys. rev. lett., 70, 1339, (1993)
[5] Adhikari, R.; Stratford, K.; Cates, M.E.; Wagner, A.J., Europhys. lett., 3, 473, (2005)
[6] Dünweg, B.; Ladd, A.J.C., Adv. polym. sci., 221, 89, (2009)
[7] Dünweg, B.; Schiller, U.D.; Ladd, A.J.C., Comput. phys. commun., 180, 605-608, (2009)
[8] Buchmann, F.M.; Petersen, W.P., BIT numer. math., 43, 519, (2003)
[9] Free Software Foundation, GSL - GNU Scientific Library - Version 1.12
[10] Ziff, R.M., Comput. phys., 12, 385, (1998)
[11] Marsaglia, G., Diehard: battery of tests of randomness
[12] Marsaglia, G., J. stat. soft., 14, (2005)
[13] Brown, R.G., Dieharder: A random number test suite – version 2.28.1
[14] Vattulainen, I.; Ala-Nissila, T.; Kankaala, K., Phys. rev. E, 52, 3205, (1995)
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