{"volume":6,"abstract":[{"lang":"eng","text":"We consider a random Schrödinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, Qr, and a random transversally periodic potential, κQt, with coupling constant κ. Using a new one-dimensional dynamical systems approach combined with Jensen's inequality in hyperbolic space (our key estimate) we obtain a fractional moment estimate proving localization for small and large κ. Together with a previous result we therefore obtain a model with two Anderson transitions, from localization to delocalization and back to localization, when increasing κ. As a by-product we also have a partially new proof of one-dimensional Anderson localization at any disorder."}],"date_updated":"2021-01-12T06:49:12Z","publist_id":"6112","oa_version":"Preprint","author":[{"full_name":"Froese, Richard","first_name":"Richard","last_name":"Froese"},{"first_name":"Darrick","last_name":"Lee","full_name":"Lee, Darrick"},{"full_name":"Sadel, Christian","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","first_name":"Christian","orcid":"0000-0001-8255-3968","last_name":"Sadel"},{"first_name":"Wolfgang","last_name":"Spitzer","full_name":"Spitzer, Wolfgang"},{"full_name":"Stolz, Günter","last_name":"Stolz","first_name":"Günter"}],"status":"public","date_created":"2018-12-11T11:50:48Z","language":[{"iso":"eng"}],"publication":"Journal of Spectral Theory","publication_status":"published","issue":"3","type":"journal_article","doi":"10.4171/JST/132","page":"557 - 600","oa":1,"_id":"1223","scopus_import":1,"date_published":"2016-01-01T00:00:00Z","citation":{"mla":"Froese, Richard, et al. “Localization for Transversally Periodic Random Potentials on Binary Trees.” <i>Journal of Spectral Theory</i>, vol. 6, no. 3, European Mathematical Society, 2016, pp. 557–600, doi:<a href=\"https://doi.org/10.4171/JST/132\">10.4171/JST/132</a>.","short":"R. Froese, D. Lee, C. Sadel, W. Spitzer, G. Stolz, Journal of Spectral Theory 6 (2016) 557–600.","ieee":"R. Froese, D. Lee, C. Sadel, W. Spitzer, and G. Stolz, “Localization for transversally periodic random potentials on binary trees,” <i>Journal of Spectral Theory</i>, vol. 6, no. 3. European Mathematical Society, pp. 557–600, 2016.","ama":"Froese R, Lee D, Sadel C, Spitzer W, Stolz G. Localization for transversally periodic random potentials on binary trees. <i>Journal of Spectral Theory</i>. 2016;6(3):557-600. doi:<a href=\"https://doi.org/10.4171/JST/132\">10.4171/JST/132</a>","chicago":"Froese, Richard, Darrick Lee, Christian Sadel, Wolfgang Spitzer, and Günter Stolz. “Localization for Transversally Periodic Random Potentials on Binary Trees.” <i>Journal of Spectral Theory</i>. European Mathematical Society, 2016. <a href=\"https://doi.org/10.4171/JST/132\">https://doi.org/10.4171/JST/132</a>.","ista":"Froese R, Lee D, Sadel C, Spitzer W, Stolz G. 2016. Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. 6(3), 557–600.","apa":"Froese, R., Lee, D., Sadel, C., Spitzer, W., &#38; Stolz, G. (2016). Localization for transversally periodic random potentials on binary trees. <i>Journal of Spectral Theory</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/JST/132\">https://doi.org/10.4171/JST/132</a>"},"intvolume":"         6","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1408.3961"}],"quality_controlled":"1","title":"Localization for transversally periodic random potentials on binary trees","department":[{"_id":"LaEr"}],"day":"01","publisher":"European Mathematical Society","year":"2016","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"01"}