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- W2964078744 abstract "Assume that $m,sinmathbb N$, $m>1$, while $f$ is a polynomial with integer coefficients, $text{deg}~f>1$, $f^{(i)}$ is the $i$th iteration of the polynomial $f$, $kappa_n$ has a discrete uniform distribution on the set ${0,1,ldots,m^n - 1}$. We are going to prove that with $n$ tending to infinity random vectors $left(frac{kappa_n}{m^n},frac{f(kappa_n) bmod m^n}{m^n},ldots,frac{f^{(s - 1)}(kappa_n) bmod m^n}{m^n}right)$ weakly converge to a vector having a continuous uniform distribution in the $s$-dimensional unit cube. Analogous results were obtained earlier only for some classes of polynomials with $sleqslant 3, text{deg}~f = 2$. The mentioned vectors represent sequential pseudorandom numbers produced by a polynomial congruential generator modulo $m^n$." @default.
- W2964078744 created "2019-07-30" @default.
- W2964078744 creator A5055448513 @default.
- W2964078744 date "2017-09-20" @default.
- W2964078744 modified "2023-09-27" @default.
- W2964078744 title "The uniform distribution of sequences generated by iterated polynomials" @default.
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