##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Ioana Dumitriu

#### UCSD

## Spectral gap in random bipartite biregular graphs and applications

##### Abstract:

The asymptotics of the second-largest eigenvalue in random regular graphs (also referred to as the ``Alon conjecture'') have been computed by Joel Friedman in his celebrated 2004 paper. Recently, a new proof of this result has been given by Charles Bordenave, using the non-backtracking operator and the Ihara-Bass formula. In the same spirit, we have been able to translate Bordenave's ideas to bipartite biregular graphs in order to calculate the asymptotical value of the second-largest pair of eigenvalues, and obtained a similar spectral gap result. Applications include community detection in equitable graphs or frames, matrix completion, and the construction of channels for efficient and tractable error-correcting codes (Tanner codes). This work is joint with Gerandy Brito and Kameron Harris.

### November 5, 2019

### 10:00 AM

### AP&M 2402

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