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- W92731399 abstract "We show that the adjacency matrix $M$ of a uniform random $d$-regular directed graph on $n$ vertices is invertible with high probability, assuming that $d=lfloor delta nrfloor$ for some fixed $deltain (0,1)$ and $n$ is large. The proof exploits both local and global symmetries of the distribution of $M$. As in the analogous work of Koml'os for i.i.d. sign matrices, we separately handle the event that $M$ has null vectors with a certain special structure, and employ an anti-concentration estimate for random walks due to ErdH{o}s. To overcome difficulties arising from the dependencies among the entries of $M$ we make use of some discrepancy properties for the digraph." @default.
- W92731399 created "2016-06-24" @default.
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- W92731399 date "2014-03-24" @default.
- W92731399 modified "2023-09-27" @default.
- W92731399 title "Random regular digraphs: Singularity and discrepancy" @default.
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