Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2403.07345 |
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Sommario:
- We consider an operator $P_V=(1+V)P$ on $\ell^2(Z^d)$, where $P$ is the transition operator of a symmetric irreducible random walk, and $V$ is a ``sparse'' potential. We first characterize the essential spectra of this operator. Secondly, we prove that all the eigenfunctions which correspond to discrete spectra decay exponentially fast. Thirdly, we give a sufficient condition for this operator to have an absolute spectral gap at the right edge of the spectra. Finally, as an application of the absolute spectral gap and the exponential decay of the eigenfunctions, we prove a limit theorem for the random walk under the Gibbs measure associated to the potential $V$.