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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.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…
math.PR2024
On Exponential Convergence of Random Variables
Dawid TarÅowski
Given the discrete-time sequence of nonnegative random variables, general dependencies between the exponential convergence of the expectations, exponential convergence of the traje…