466 citations · 2.7k across the 81 of their papers we have counts for
5 papers · 2 filters
Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count
Gregory Berkolaiko, Hillel Raz, Uzy Smilansky
The nodal domains of eigenvectors of the discrete Schrodinger operator on simple, finite and connected graphs are considered. Courant's well known nodal domain theorem applies in t…
Note on the role of symmetry in scattering from isospectral graphs and drums
Ram Band, Adam Sawicki, Uzy Smilansky
We discuss scattering from pairs of isospectral quantum graphs constructed using the method described in [1, 2]. It was shown in [3] that scattering matrices of such graphs have th…
Critical partitions and nodal deficiency of billiard eigenfunctions
Gregory Berkolaiko, Peter Kuchment, Uzy Smilansky
The paper addresses the the number of nodal domains for eigenfunctions of Schrödinger operators with Dirichlet boundary conditions in bounded domains. In dimension one, the th e…
Periodic Walks on Large Regular Graphs and Random Matrix Theory
Idan Oren, Uzy Smilansky
We study the distribution of the number of (non-backtracking) periodic walks on large regular graphs. We propose a formula for the ratio between the variance of the number of -p…
On the connection between the number of nodal domains on quantum graphs and the stability of graph partitions
Ram Band, Gregory Berkolaiko, Hillel Raz +1
Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic eigenfunc…