3 citations · 5 across the 8 of their papers we have counts for
10 papers
Almost sharp lower bound for the nodal volume of harmonic functions
Alexander Logunov, Lakshmi Priya, Andrea Sartori
This paper focuses on a relation between the growth of harmonic functions and the Hausdorff measure of their zero sets. Let be a real-valued harmonic function in …
On the universality of the Nazarov-Sodin constant
Andrea Sartori
We study the number of connected components of non-Gaussian random spherical harmonics on the two dimensional sphere . We prove that the expectation of the nodal doma…
On the behavior of nodal lines near the boundary for Laplace eigenfunctions on the square
Oleksiy Klurman, Andrea Sartori
We are interested in the effect of Dirichlet boundary conditions on the nodal length of Laplace eigenfunctions. We study random Gaussian Laplace eigenfunctions on the two dimension…
Expected nodal volume for non-Gaussian random band-limited functions
Zakhar Kabluchko, Andrea Sartori, Igor Wigman
The asymptotic law for the expected nodal volume of random non-Gaussian monochromatic band-limited functions is determined in vast generality. Our methods combine microlocal analyt…
Asymptotic nodal length and log-integrability of toral eigenfunctions
Andrea Sartori
We study the nodal set of Laplace eigenfunctions on the flat torus . We prove an asymptotic law for the nodal length of such eigenfunctions, under some growth as…
Nodal set of monochromatic waves satisfying the Random Wave Model
Álvaro Romaniega, Andrea Sartori
We construct deterministic solutions to the Helmholtz equation in which behave accordingly to the Random Wave Model. We then find the number of their nodal domains,…
Spectral quasi correlations and phase-transitions for the nodal length of Arithmetic Random Waves
Andrea Sartori
Spectral quasi correlations are small sums of lattice points lying on the same circle; we show that, for generic integers representable as the sum of two squares, there are no spec…
Planck-scale number of nodal domains for toral eigenfunctions
Andrea Sartori
We study the number of nodal domains in balls shrinking slightly above the Planck scale for "generic" toral eigenfunctions. We prove that, up to the natural scaling, the nodal doma…
Mass distribution for toral eigenfunctions via Bourgain's de-randomisation
Andrea Sartori
We study the problem of mass distribution of Laplacian eigenfunctions in shrinking balls for the standard flat torus . By averaging over the…
Least primitive root and simultaneous power-non residues
Andrea Sartori
Let be a prime and let be the least primitive root modulo . We prove that for any and large enough the bound \begin{align} g(p)\ll p^{\frac{1}{4\sqrt{e}}+ε}…