3 citations · 9 across the 6 of their papers we have counts for
9 papers
Eisenstein Series and Breakdown of Semiclassical Correspondence
Shimon Brooks
We consider certain Lagrangian states associated to unstable horocycles on the modular surface , and show that for sufficiently large logarit…
Norms of Eigenfunctions on Regular Graphs and on the Sphere
Shimon Brooks, Etienne Le Masson
We prove upper bounds on the norms of eigenfunctions of the discrete Laplacian on regular graphs. We then apply these ideas to study the norms of joint eigenfunctions o…
Quantum Ergodicity and Averaging Operators on the Sphere
Shimon Brooks, Etienne Le Masson, Elon Lindenstrauss
We prove quantum ergodicity for certain orthonormal bases of , consisting of joint eigenfunctions of the Laplacian on and the discrete averaging o…
Eisenstein Quasimodes and QUE
Shimon Brooks
We consider the question of Quantum Unique Ergodicity for quasimodes on surfaces of constant negative curvature, and conjecture the order of quasimodes that should satisfy QUE. We…
Logarithmic-scale Quasimodes that do not Equidistribute
Shimon Brooks
Given any compact hyperbolic surface , and a closed geodesic on , we construct of a sequence of quasimodes on whose microlocal lifts concentrate positive mass on the geod…
Joint Quasimodes, Positive Entropy, and Quantum Unique Ergodicity
Shimon Brooks, Elon Lindenstrauss
We study joint quasimodes of the Laplacian and one Hecke operator on compact congruence surfaces, and give conditions on the orders of the quasimodes that guarantee positive entrop…
Partially Localized Quasimodes in Large Subspaces
Shimon Brooks
We consider spaces of high-energy quasimodes for the Laplacian on a compact hyperbolic surface, and show that when the spaces are large enough, one can find quasimodes that exhibit…
Graph Eigenfunctions and Quantum Unique Ergodicity
Shimon Brooks, Elon Lindenstrauss
We apply the techniques of our previous paper to study joint eigenfunctions of the Laplacian and one Hecke operator on compact congruence surfaces, and joint eigenfunctions of the…
Non-localization of eigenfunctions on large regular graphs
Shimon Brooks, Elon Lindenstrauss
We give a delocalization estimate for eigenfunctions of the discrete Laplacian on large -regular graphs, showing that any subset of the graph supporting of the mass…