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

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove several results of concentration for eigenfunctions in Toeplitz quantization. Under mild regularity assumptions, we prove that eigenfunctions are $O(\exp(-cN^{\delta}))$ away from the corresponding level set of the symbol, where $N$ is the inverse semiclassical parameter and $0\delta1$ 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.
Classification : 32J27, 32A36, 32W30, 81Q10, 81Q20, 82B10
Keywords: compact quantizable Kähler manifolds, Berezin-Toeplitz operators 
@article{DOCMA_2020__25__a29,
     author = {Deleporte, Alix},
     title = {Fractional {Exponential} {Decay} in the {Forbidden} {Region} for {Toeplitz} {Operators}},
     journal = {Documenta mathematica},
     pages = {1315--1351},
     publisher = {mathdoc},
     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a29/}
}
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Deleporte, Alix. Fractional Exponential Decay in the Forbidden Region for Toeplitz Operators. Documenta mathematica, Tome 25 (2020), pp. 1315-1351. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a29/