A non-backtracking walk on a graph is a directed path such that no edge is the inverse of its
preceding edge. The non-backtracking matrix of a graph is indexed by its directed edges …

We study a random graph model called the “stochastic block model” in statistics and the
“planted partition model” in theoretical computer science. In its simplest form, this is a …

Recent progress in combinatorial random matrix theory Page 1 Probability Surveys Vol. 18 (2021)
179–200 ISSN: 1549-5787 https://doi.org/10.1214/20-PS346 Recent progress in combinatorial …

We prove that Ising models on the hypercube with general quadratic interactions satisfy a
Poincaré inequality with respect to the natural Dirichlet form corresponding to Glauber …

We establish bounds on the spectral radii for a large class of sparse random matrices, which
includes the adjacency matrices of inhomogeneous Erdős–Rényi graphs. Our error bounds …

Abstract An (n, d, λ)-graph is ad regular graph on n vertices in which the absolute value of
any nontrivial eigenvalue is at most λ. For any constant d≥ 3, ϵ> 0 and all sufficiently large …

The Sum-of-Squares (SoS) hierarchy of semidefinite programs is a powerful algorithmic
paradigm which captures state-of-the-art algorithmic guarantees for a wide array of …

We consider random d‐regular graphs on N vertices, with degree d at least (log N) 4. We
prove that the Green's function of the adjacency matrix and the Stieltjes transform of its …

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 …

Let X be a compact connected hyperbolic surface, that is, a closed connected orientable
smooth surface with a Riemannian metric of constant curvature-1. For each n∈ N, let X n be …