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A new proof of Friedman’s second eigenvalue Theorem and its extensions

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If you have a question about this talk, please contact Perla Sousi.

It was conjectured by Alon and proved by Friedman that a random d-regular graph has nearly the largest possible spectral gap, more precisely, the largest absolute value of the non-trivial eigenvalues of its adjacency matrix is at most 2 √ ( d − 1) + o(1) with probability tending to one as the size of the graph tends to infinity. We will discuss a new method to prove this statement and give some extensions to random lifts and related models.

This talk is part of the Probability series.

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