Geodesic
Fractional Exponential Decay in the Forbidden Region for Toeplitz Operators
Documenta mathematica, Tome 25 (2020), pp. 1315-1351

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We prove several results of concentration for eigenfunctions in Toeplitz quantization. Under mild regularity assumptions, we prove that eigenfunctions are O(exp(−cNδ)) away from the corresponding level set of the symbol, where N is the inverse semiclassical parameter and 0<δ<1 depends on the regularity. As an application, we prove a precise bound for the free energy of spin systems at high temperatures, sharpening a result of Lieb.
DOI : 10.4171/dm/778
Classification : 32A36, 32J27, 32W30, 81Q10, 81Q20, 82B10
Mots-clés : compact quantizable Kähler manifolds, Berezin-Toeplitz operators 
Alix Deleporte. Fractional Exponential Decay in the Forbidden Region for Toeplitz Operators. Documenta mathematica, Tome 25 (2020), pp. 1315-1351. doi: 10.4171/dm/778
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     author = {Alix Deleporte},
     title = {Fractional {Exponential} {Decay} in the {Forbidden} {Region} for {Toeplitz} {Operators}},
     journal = {Documenta mathematica},
     pages = {1315--1351},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/778},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/778/}
}
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