A d-regular graph has largest or first (adjacency matrix) eigenvalue 1 = d. Consider for an even d 4, a random d-regular graph model formed from d/2 uniform, independent permutat...
A d-regular graph has largest or first (adjacency matrix) eigenvalue 1 = d. In this paper we show the following conjecture of Alon. Fix an integer d > 2 and a real > 0. Then...
We study here the spectra of random lifts of graphs. Let G be a finite connected graph, and let the infinite tree T be its universal cover space. If λ1 and ρ are the spectral ...
In the setting of secure computation, a set of parties wish to securely compute some function of their inputs, in the presence of an adversary. The adversary in question may be st...
One of the major tasks of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on the true evolu...