3 papers
math.PR2026
On the sum-of-digits measures and Cusick's conjecture via stopped random walks
Dawid TarÅowski
Let denote the number of ones in the binary expansion of a natural number . For any and , let denote the asymptoti…
math.ST2025
Conditional uncorrelation equals independence
Dawid TarÅowski
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian produ…
math.PR2025
Sleeping Beauty and Markov chains
Dawid TarÅowski
Sleeping Beauty Problem (SBP) is a probability puzzle which has created much confusion in the literature. In this paper we present the analysis of SBP with use of ergodic Markov ch…