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arXiv · 1804.07808

Spectral gap in random bipartite biregular graphs and applications

Gerandy Brito·Ioana Dumitriu·Kameron Decker Harris
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Abstract

We prove an analogue of Alon's spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara-Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there exists a spectral gap for the non-backtracking matrix. A byproduct of our main theorem is that random rectangular zero-one matrices with fixed row and column sums are full-rank with high probability. Finally, we illustrate applications to community detection, coding theory, and deterministic matrix completion.

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Gerandy Brito, Ioana Dumitriu, Kameron Decker Harris. 2018-04-20. Spectral gap in random bipartite biregular graphs and applications. https://doi.org/10.1017/s0963548321000249

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