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 Mathematics , 2011, Abstract: In this paper we construct a pseudorandom multisequence $(x_{n_1,...,n_r})$ based on $k$th-order linear recurrences modulo $p$, such that the discrepancy of the $s$-dimensional multisequence $(x_{n_1+i_1,...,n_r+i_r})_{1 \leq i_j \leq s_j, 1 \leq j \leq r}$ $1 \leq n_j \leq N_j, 1 \leq j \leq r$ is equal to $O((N_1 ... N_r)^{-1/2} \ln^{s+3r}(N_1 ... N_r))$, where $s=s_1 ... s_r$, for all $N_1,...,N_r$ with $1 < N_1 ... N_r \leq p^k  Mathematics , 2012, Abstract: In this paper, we focus on analyzing the period distribution of the inversive pseudorandom number generators (IPRNGs) over finite field$({\rm Z}_{N},+,\times)$, where$N>3$is a prime. The sequences generated by the IPRNGs are transformed to 2-dimensional linear feedback shift register (LFSR) sequences. By employing the generating function method and the finite field theory, the period distribution is obtained analytically. The analysis process also indicates how to choose the parameters and the initial values such that the IPRNGs fit specific periods. The analysis results show that there are many small periods if$N$is not chosen properly. The experimental examples show the effectiveness of the theoretical analysis.  Robert M. Ziff Physics , 1997, DOI: 10.1063/1.168692 Abstract: It is shown how correlations in the generalized feedback shift-register (GFSR) random-number generator are greatly diminished when the number of feedback taps is increased from two to four (or more) and the tap offsets are lengthened. Simple formulas for producing maximal-cycle four-tap rules from available primitive trinomials are given, and explicit three- and four-point correlations are found for some of those rules. A number of generators are also tested using a simple but sensitive random-walk simulation that relates to a problem in percolation theory. While virtually all two-tap generators fail this test, four-tap generators with offset greater than about 500 pass it, have passed tests carried out by others, and appear to be good multi-purpose high-quality random-number generators.  Physics , 1995, DOI: 10.1142/S0129183195000642 Abstract: We report large systematic errors in Monte Carlo simulations of the tricritical Blume-Capel model using single spin Metropolis updating. The error, manifest as a$20\%\$ asymmetry in the magnetisation distribution, is traced to the interplay between strong triplet correlations in the shift register random number generator and the large tricritical clusters. The effect of these correlations is visible only when the system volume is a multiple of the random number generator lag parameter. No such effects are observed in related models.