20 citations · 52 across the 37 of their papers we have counts for
8 papers · 1 filter
Construction of normal numbers via generalized prime power sequences
Manfred G. Madritsch, Robert F. Tichy
In the present paper the authors construct normal numbers in base by concatenating -adic expansions of prime powers with and .
A central limit theorem for Latin hypercube sampling with dependence and application to exotic basket option pricing
Christoph Aistleitner, Markus Hofer, Robert Tichy
We consider the problem of estimating , where denotes a random vector with uniformly distributed marginals. In general, Latin…
On permutations of lacunary series
Christoph Aistleitner, Istvan Berkes, Robert Tichy
It is a well known fact that for periodic measurable and rapidly increasing the sequence behaves like a sequence of independent, identic…
On the law of the iterated logarithm for permuted lacunary sequences
Christoph Aistleitner, Istvan Berkes, Robert Tichy
It is known that for any smooth periodic function the sequence behaves like a sequence of i.i.d.\ random variables, for example, it satisfies the central l…
On the system and probabilistic number theory
Christoph Aistleitner, Istvan Berkes, Robert Tichy
Let be a measurable function satisfying \begin{equation*} f(x+1)=f(x), \qquad \int_0^1 f(x)\, dx=0, \qquad \int_0^1 f^2(x)\, dx<\infty. \end{equatio…
On sums of S-integers of bounded norm
Christopher Frei, Robert F. Tichy, Volker Ziegler
We prove an asymptotic formula for the number of S-integers in a number field K that can be represented by a sum of n S-integers of bounded norm.
Ergodic properties of β-adic Halton sequences
Markus Hofer, Maria Rita Iacò, Robert Tichy
We investigate a parametric extension of the classical s-dimensional Halton sequence, where the bases are special Pisot numbers. In a one- dimensional setting the properties of suc…
Uniform Distribution of Prime Powers and sets of Recurrence and van der Corput sets in Z^k
Vitaly Bergelson, Grigori Kolesnik, Manfred Madritsch +2
We establish new results on sets of recurrence and van der Corput sets in Z^k which refine and unify some of the previous results obtained by Sarkozy, Furstenberg, Kamae and Mendes…