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.