[{"publist_id":"6112","issue":"3","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."}],"type":"journal_article","author":[{"full_name":"Froese, Richard","last_name":"Froese","first_name":"Richard"},{"full_name":"Lee, Darrick","first_name":"Darrick","last_name":"Lee"},{"full_name":"Sadel, Christian","orcid":"0000-0001-8255-3968","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","last_name":"Sadel","first_name":"Christian"},{"last_name":"Spitzer","first_name":"Wolfgang","full_name":"Spitzer, Wolfgang"},{"last_name":"Stolz","first_name":"Günter","full_name":"Stolz, Günter"}],"volume":6,"oa_version":"Preprint","date_created":"2018-12-11T11:50:48Z","date_updated":"2021-01-12T06:49:12Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1223","year":"2016","intvolume":" 6","publisher":"European Mathematical Society","department":[{"_id":"LaEr"}],"title":"Localization for transversally periodic random potentials on binary trees","status":"public","publication_status":"published","month":"01","day":"01","scopus_import":1,"doi":"10.4171/JST/132","date_published":"2016-01-01T00:00:00Z","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1408.3961"}],"citation":{"ama":"Froese R, Lee D, Sadel C, Spitzer W, Stolz G. Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. 2016;6(3):557-600. doi:10.4171/JST/132","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., & Stolz, G. (2016). Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. European Mathematical Society. https://doi.org/10.4171/JST/132","ieee":"R. Froese, D. Lee, C. Sadel, W. Spitzer, and G. Stolz, “Localization for transversally periodic random potentials on binary trees,” Journal of Spectral Theory, vol. 6, no. 3. European Mathematical Society, pp. 557–600, 2016.","mla":"Froese, Richard, et al. “Localization for Transversally Periodic Random Potentials on Binary Trees.” Journal of Spectral Theory, vol. 6, no. 3, European Mathematical Society, 2016, pp. 557–600, doi:10.4171/JST/132.","short":"R. Froese, D. Lee, C. Sadel, W. Spitzer, G. Stolz, Journal of Spectral Theory 6 (2016) 557–600.","chicago":"Froese, Richard, Darrick Lee, Christian Sadel, Wolfgang Spitzer, and Günter Stolz. “Localization for Transversally Periodic Random Potentials on Binary Trees.” Journal of Spectral Theory. European Mathematical Society, 2016. https://doi.org/10.4171/JST/132."},"oa":1,"publication":"Journal of Spectral Theory","page":"557 - 600","quality_controlled":"1"}]