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- W3084164468 abstract "Gao, Jackson, and Seward (see arXiv:1201.0513) proved that every countably infinite group $Gamma$ admits a nonempty free subshift $X subseteq {0,1}^Gamma$. Furthermore, a theorem of Seward and Tucker-Drob (see arXiv:1402.4184) implies that every countably infinite group $Gamma$ admits a free subshift $X subseteq {0,1}^Gamma$ that supports an invariant probability measure. Aubrun, Barbieri, and Thomasse (see arXiv:1507.03369) used the Lovasz Local Lemma to give a short alternative proof of the Gao--Jackson--Seward theorem. Recently, Elek (see arXiv:1702.01631) followed another approach involving the Lovasz Local Lemma to obtain a different proof of the existence of free subshifts with invariant probability measures for finitely generated sofic groups. Using the measurable version of the Lovasz Local Lemma for shift actions established by the author (see arXiv:1604.07349), we give a short alternative proof of the existence of such subshifts for arbitrary groups. Moreover, we can find such subshifts in any nonempty invariant open set." @default.
- W3084164468 created "2020-09-14" @default.
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- W3084164468 date "2017-02-09" @default.
- W3084164468 modified "2023-09-27" @default.
- W3084164468 title "Free Subshifts with Invariant Measures" @default.
- W3084164468 hasPublicationYear "2017" @default.
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