Title: Limiting eigenvalue distribution for the non-backtracking matrix of an Erdos-Renyi random graph
Speaker: Philip Matchett Wood (University of Wisconsin)
Abstract: A non-backtracking random walk on a graph is a directed walk with the constraint that the last edge crossed may not be immediately crossed again in the opposite direction. This talk will give a precise description of the eigenvalues of the adjacency matrix for the non-backtracking walk when the underlying graph is an Erdos-Renyi random graph on $n$ vertices, where edges present independently with probability $p$. We allow $p$ to be constant or decreasing with $n$, so long as $p\sqrt{n}$ tends to infinity. The key ideas in the proof are partial derandomization, applying the Tao-Vu Replacement Principle in a novel context, and showing that partial derandomization may be interpreted as a perturbation, allowing one to apply the Bauer-Fike Theorem.
Joint work with Ke Wang at HKUST (Hong Kong University of Science and Technology).
