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13
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0012692651
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W. Selke, A.L. Talapov, and L.N. Shchur, Pis’ma Zh. Éksp. Teor. Fiz. 85, 1144 (1983) [JETP Lett. 58, 665 (1993)].
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JETP Lett.
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Selke, W.1
Talapov, A.L.2
Shchur, L.N.3
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20
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85037214388
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J. Stat. Phys. 30, 2 (1983), special issue, edited by G.W. Weiss and R.J. Rubin; E.W. Montroll and M.F. Shlesinger, in Nonequilibrium Phenomena II: From Stochastics to Hydrodynamics, edited by J.L. Lebowitz and E.W. Montroll (Elsevier, Amsterdam, 1984)
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J. Stat. Phys. 30, 2 (1983), special issue, edited by G.W. Weiss and R.J. Rubin; E.W. Montroll and M.F. Shlesinger, in Nonequilibrium Phenomena II: From Stochastics to Hydrodynamics, edited by J.L. Lebowitz and E.W. Montroll (Elsevier, Amsterdam, 1984).
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21
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85037220732
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There are many ways to construct the sequences (Formula presented) for the processors one through m. We used random numbers (Formula presented) generated by a single pseudorandom number generator to make nonoverlapping sequences (Formula presented) (Formula presented) and so forth. Other possibilities for constructing the sequences are given in, e.g
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There are many ways to construct the sequences (Formula presented) for the processors one through m. We used random numbers (Formula presented) generated by a single pseudorandom number generator to make nonoverlapping sequences (Formula presented) (Formula presented) and so forth. Other possibilities for constructing the sequences are given in, e.g.
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26
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0001337952
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G. Slade, Am. Sci. 84, 146 (1996).
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(1996)
Am. Sci.
, vol.84
, pp. 146
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Slade, G.1
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27
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85037230026
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Use of the intersection test to study more than two random walkers is also possible, although rigorous mathematical bounds for (Formula presented) in this case are not available (see Refs. 17 18
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Use of the intersection test to study more than two random walkers is also possible, although rigorous mathematical bounds for (Formula presented) in this case are not available (see Refs. 1718).
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28
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33646983638
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H. Larralde, P. Trunfio, S. Havlin, H.E. Stanley, and G.H. Weiss, Phys. Rev. A 45, 7128 (1992).
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(1992)
Phys. Rev. A
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, pp. 7128
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Larralde, H.1
Trunfio, P.2
Havlin, S.3
Stanley, H.E.4
Weiss, G.H.5
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29
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85037208563
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Equation (2) is just one rational approach to consider the convergence of an exponent which characterizes power-law behavior. Another possibility given in Ref. 17 was found to yield consistent results in the asymptotic limit
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Equation (2) is just one rational approach to consider the convergence of an exponent which characterizes power-law behavior. Another possibility given in Ref. 17 was found to yield consistent results in the asymptotic limit.
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36
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85037243979
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To determine the exponent, there are various ways which yield essentially identical results. Estimation of the error bars is a different matter. Use of linear regression is one possibility, but this approach provides an error estimate that is unreasonably small. To obtain a more realistic estimate, we determined the error bars (given in Table I) on the basis of fluctuations in the running exponents
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To determine the exponent, there are various ways which yield essentially identical results. Estimation of the error bars is a different matter. Use of linear regression is one possibility, but this approach provides an error estimate that is unreasonably small. To obtain a more realistic estimate, we determined the error bars (given in Table I) on the basis of fluctuations in the running exponents.
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38
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0029308078
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I. Vattulainen, K. Kankaala, J. Saarinen, and T. Ala-Nissila, Comput. Phys. Commun. 86, 209 (1995).
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(1995)
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, pp. 209
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Vattulainen, I.1
Kankaala, K.2
Saarinen, J.3
Ala-Nissila, T.4
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40
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0003657590
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Addison-Wesley, Reading, MA
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D.E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms, 2nd ed. (Addison-Wesley, Reading, MA, 1981).
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(1981)
The Art of Computer Programming, Volume 2: Seminumerical Algorithms, 2nd ed.
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Knuth, D.E.1
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41
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85037194533
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To determine (Formula presented), we calculated a given correlation function (Formula presented) of RANLUX4 ten times with (Formula presented) samples each up to (Formula presented). For each of these, we calculated (Formula presented) (Formula presented), with respect to (an independent calculation of) (Formula presented) of RANLUX4 with M samples. Then (Formula presented) is simply the mean of (Formula presented). The same procedure was carried out for all correlation functions (Formula presented) (Formula presented) and (Formula presented)
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To determine (Formula presented), we calculated a given correlation function (Formula presented) of RANLUX4 ten times with (Formula presented) samples each up to (Formula presented). For each of these, we calculated (Formula presented) (Formula presented), with respect to (an independent calculation of) (Formula presented) of RANLUX4 with M samples. Then (Formula presented) is simply the mean of (Formula presented). The same procedure was carried out for all correlation functions (Formula presented) (Formula presented) and (Formula presented)
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44
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0031599234
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references therein
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For theoretical work on parallel random number generation, see K. Entacher, ACM Trans. Model. Comput. Simul. 8, 61 (1998), and references therein.
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(1998)
ACM Trans. Model. Comput. Simul.
, vol.8
, pp. 61
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Entacher, K.1
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