91 citations · 323 across the 30 of their papers we have counts for
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Quantum Ergodicity on large hyperbolic surfaces for local and pseudolocal operators
Nalini Anantharaman, Soumyajit Saha
We prove a quantum ergodicity theorem for sequences of closed hyperbolic surfaces converging to the Poincaré disc in the Benjamini-Schramm sense. Assuming a uniform lower bound on…
Typical hyperbolic surfaces have a spectral gap greater than
Nalini Anantharaman, Laura Monk
In this article, we prove that typical hyperbolic surfaces, sampled with the Weil-Petersson probability measure, have a spectral gap at least . This is an intermediate res…
Friedman-Ramanujan functions in random hyperbolic geometry and application to spectral gaps I
Nalini Anantharaman, Laura Monk
In this series of articles, we analyse the level-sets of length functions on the moduli space of compact hyperbolic surfaces of fixed genus. This work ultimately culminates in a pr…
Empirical spectral measures of quantum graphs in the Benjamini-Schramm limit
Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri +1
We introduce the notion of Benjamini-Schramm convergence for quantum graphs. This notion of convergence, intended to play the role of the already existing notion for discrete graph…
Absolutely Continuous Spectrum for Quantum Trees
Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri +1
We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling…
Recent results of quantum ergodicity on graphs and further investigation
Nalini Anantharaman, Mostafa Sabri
We outline some recent proofs of quantum ergodicity on large graphs and give new applications in the context of irregular graphs. We also discuss some remaining questions.