Dawid Tarłowski

activity

20242026

collaborators

5 papers

math.NT2026

The equality cases $P_{t} (N) = \frac{1}{2}$ for the deconvolved sum-of-digits measures

Dawid Tarłowski

Let $s (n)$ denote the number of ones in the binary expansion of an integer $n \in N$ , and let $μ_{t}$ be the probability measure on $Z$ defined by the asymptotic dens…

math.PR2026

On the sum-of-digits measures and Cusick's conjecture via stopped random walks

Dawid Tarłowski

Let $s (n)$ denote the number of ones in the binary expansion of a natural number $n \in N$ . For any $t \in N$ and $d \in Z$ , let $μ_{t} (d)$ denote the asymptotic…

math.PR2025

Sleeping Beauty and Markov chains

Dawid Tarłowski

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…

math.PR2024

On Exponential Convergence of Random Variables

Dawid Tarłowski

Given the discrete-time sequence of nonnegative random variables, general dependencies between the exponential convergence of the expectations, exponential convergence of the traje…

math.ST2024

Conditional uncorrelation equals independence

Dawid Tarłowski

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…

The equality cases Pt​(N)=21​ for the deconvolved sum-of-digits measures

On the sum-of-digits measures and Cusick's conjecture via stopped random walks

Sleeping Beauty and Markov chains

On Exponential Convergence of Random Variables

Conditional uncorrelation equals independence

The equality cases $P_{t} (N) = \frac{1}{2}$ for the deconvolved sum-of-digits measures