M. Levin

activity

20112020

most citedOn the lower bound of the discrepancy of

(t, s)

sequences: II

6 citations · 8 across the 10 of their papers we have counts for

collaborators

12 papers

math.NT2020

Central Limit Theorem for $(t, s)$ -sequences, I

Mordechay B. Levin

Let $(X_{n})_{n \geq 0}$ be a digital $(t, s)$ -sequence in base $2$ , $P_{m} = (X_{n})_{n = 0}^{2^{m} - 1}$ , and let $D (P_{m}, Y)$ be the local discrepancy of $\mathcal{P}_m…

math.NT2020

On the upper bound of the $L_{2}$ -discrepancy of Halton's sequence

Mordechay B. Levin

Let $(H (n))_{n \geq 0}$ be a $2 -$ dimensional Halton's sequence. Let $D_{2} ((H (n))_{n = 0}^{N - 1})$ be the $L_{2}$ -discrepancy of $(H_{n})_{n = 0}^{N - 1}$ . It is known that $\limsup_{N…

math.NT2020

Temporal Central Limit Theorem for Multidimensional Adding Machine

Mordechay B. Levin

Let $p_{1}, ..., p_{s + 1}$ be distinct primes and let $T_{p_{i}}$ be the von Niemann - Kakutani adding machine $(1 \leq i \leq s)$ , $T_{\mathcal{P}}(\mathbf{x}) =(T_{p_1}(x_1),..., T_{p_s…

math.NT2019

On a bounded remainder set for $(t, s)$ sequences I

Mordechay B. Levin

Let $x_{0}, x_{1}, ...$ be a sequence of points in $[0, 1)^{s}$ . A subset $S$ of $[0, 1)^{s}$ is called a bounded remainder set if there exist two real numbers $a$ and $C$ such tha…

math.NT2018

On a bounded remainder set for a digital Kronecker sequence

Mordechay B. Levin

Let $x_{0}, x_{1}, ...$ be a sequence of points in $[0, 1)^{s}$ . A subset $S$ of $[0, 1)^{s}$ is called a bounded remainder set if there exist two real numbers $a$ and $C$ such tha…

math.NT2018

On the upper bound of the $L_{p}$ discrepancy of Halton's sequence and the Central Limit Theorem for Hammersley's net

Mordechay B. Levin

Let $(H_{s} (n))_{n \geq 1}$ be an $s -$ dimensional Halton's sequence, and let $H_{s + 1, N} = (H_{s} (n), n / N)_{n = 0}^{N - 1}$ be the $s + 1 -$ dimensional Hammersley point set. Let $D(\m…

Central Limit Theorem for (t,s)-sequences, I

On the upper bound of the L2​-discrepancy of Halton's sequence

Temporal Central Limit Theorem for Multidimensional Adding Machine

On a bounded remainder set for (t,s) sequences I

On a bounded remainder set for a digital Kronecker sequence

On the upper bound of the Lp​ discrepancy of Halton's sequence and the Central Limit Theorem for Hammersley's net

Central Limit Theorem for $(t, s)$ -sequences, I

On the upper bound of the $L_{2}$ -discrepancy of Halton's sequence

On a bounded remainder set for $(t, s)$ sequences I

On the upper bound of the $L_{p}$ discrepancy of Halton's sequence and the Central Limit Theorem for Hammersley's net