Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2601.17738 |
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Sommario:
- We study the asymptotic behavior of Markov operators $P_μ$ defined by convolution with a probability measure $μ$ on the unit circle $\mathbb T$. We prove that when $μ$ is adapted, $P_μ$ satisfies Doeblin's condition if and only if some power $μ^k$ is non-singular. We give an example of a symmetric probability measure $μ$ on $\mathbb T$, such that the reversible stationary chain induced by $P_μ$ is $ρ$-mixing, but $P_μ$ does not satisfy Doeblin's condition. We look at the spectra of $P_μ$ in the different $L_p$ spaces when $P_μ$ is, or is not, $ρ$-mixing.