4 papers
Eigenvalues and spectral gap in sparse random simplicial complexes
Shaked Leibzirer, Ron Rosenthal
We consider the adjacency operator of the Linial-Meshulam model for random dimensional simplicial complexes on vertices, where each cell is added indepen…
On the Spectrum of Dense Random Geometric Graphs
Kartick Adhikari, Robert J. Adler, Omer Bobrowski +1
In this paper we study the spectrum of the random geometric graph , in a regime where the graph is dense and highly connected. In the \erdren random graph it is we…
Eigenvector correlations in the complex Ginibre ensemble
Nicholas Crawford, Ron Rosenthal
The complex Ginibre ensemble is an non-Hermitian random matrix over with i.i.d. complex Gaussian entries normalized to have mean zero and variance . U…
Stabilization of DLA in a wedge
Eviatar B. Procaccia, Ron Rosenthal, Yuan Zhang
We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than , there is some such that almost sure…