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pro vyhledávání: '"Masson, Etienne Le"'
Autor:
Masson, Etienne Le, Sahlsten, Tuomas
We give a quantitative estimate for the quantum mean absolute deviation on hyperbolic surfaces of finite area in terms of geometric parameters such as the genus, number of cusps and injectivity radius. It implies a delocalisation result of quantum er
Externí odkaz:
http://arxiv.org/abs/2006.14935
Publikováno v:
Geometric and Functional Analysis GAFA 31, 62-110 (2021)
We give upper bounds for $L^p$ norms of eigenfunctions of the Laplacian on compact hyperbolic surfaces in terms of a parameter depending on the growth rate of the number of short geodesic loops passing through a point. When the genus $g \to +\infty$,
Externí odkaz:
http://arxiv.org/abs/1912.09961
We investigate the asymptotic behavior of eigenfunctions of the Laplacian on Riemannian manifolds. We show that Benjamini-Schramm convergence provides a unified language for the level and eigenvalue aspects of the theory. As a result, we present a ma
Externí odkaz:
http://arxiv.org/abs/1810.05601
Autor:
Masson, Etienne Le, Sabri, Mostafa
This article is concerned with properties of delocalization for eigenfunctions of Schr\"odinger operators on large finite graphs. More specifically, we show that the eigenfunctions have a large support and we assess their lp-norms. Our estimates hold
Externí odkaz:
http://arxiv.org/abs/1809.07078
Autor:
Brooks, Shimon, Masson, Etienne Le
We prove upper bounds on the $L^p$ norms of eigenfunctions of the discrete Laplacian on regular graphs. We then apply these ideas to study the $L^p$ norms of joint eigenfunctions of the Laplacian and an averaging operator over a finite collection of
Externí odkaz:
http://arxiv.org/abs/1710.10922
Autor:
Masson, Etienne Le, Sahlsten, Tuomas
Publikováno v:
Duke Math. J. 166, no. 18 (2017), 3425-3460
We present a quantum ergodicity theorem for fixed spectral window and sequences of compact hyperbolic surfaces converging to the hyperbolic plane in the sense of Benjamini and Schramm. This addresses a question posed by Colin de Verdi\`{e}re. Our the
Externí odkaz:
http://arxiv.org/abs/1605.05720
Publikováno v:
Int Math Res Notices (2016) 2016 (19): 6034-6064
We prove quantum ergodicity for certain orthonormal bases of $L^2(\mathbb{S}^2)$, consisting of joint eigenfunctions of the Laplacian on $\mathbb{S}^2$ and the discrete averaging operator over a finite set of rotations, generating a free group. If in
Externí odkaz:
http://arxiv.org/abs/1505.03887
Publikováno v:
Duke Math. J. 164, no. 4 (2015), 723-765
We propose a version of the Quantum Ergodicity theorem on large regular graphs of fixed valency. This is a property of delocalization of "most" eigenfunctions. We consider expander graphs with few short cycles (for instance random large regular graph
Externí odkaz:
http://arxiv.org/abs/1304.4343
Autor:
Masson, Etienne Le
Publikováno v:
Ann. Henri Poincar\'e 15 (2014), no. 9, 1697-1732
In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol classes an
Externí odkaz:
http://arxiv.org/abs/1302.5387