Random regular digraphs: singularity and spectrum

Tuesday, October 27, 2015 -
3:00pm to 4:00pm
Please note special day (Tuesday).    We consider two random matrix ensembles associated to large random regular digraphs: (1) the 0/1 adjacency matrix, and (2) the adjacency matrix with iid bounded edge weights. Motivated by universality conjectures, we show that the spectral distribution for the latter ensemble is asymptotically described by the circular law, assuming the graph has degree linear in the number of vertices. Towards establishing the same result for the unweighted adjacency matrix, we prove that it is invertible with high probability, even for sparse digraphs with degree growing only poly-logarithmically.
Speaker: 
Nicholas Cook
UCLA
Event Location: 
Fine Hall 214