Various applications involve assigning discrete label values to a collection of objects based
on some pairwise noisy data. Due to the discrete—and hence nonconvex—structure of the …

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 …

We consider the community detection problem in sparse random hypergraphs. Angelini et
al. in [6] conjectured the existence of a sharp threshold on model parameters for community …

We propose a new, efficiently solvable hierarchy of semidefinite programming relaxations for
inference problems. As test cases, we consider the problem of community detection in block …

Given an underlying graph, we consider the following dynamics: Initially, each node locally
chooses a value in {-1,1\}, uniformly at random and independently of other nodes. Then, in …

In this paper, we study the spectra of regular hypergraphs following the definitions from Feng
and Li (1996). Our main result is an analog of Alon's conjecture for the spectral gap of the …

We study the problem of efficiently refuting the k-colorability of a graph, or equivalently,
certifying a lower bound on its chromatic number. We give formal evidence of average-case …

Consider the following asynchronous, opportunistic communication model over a graph $ G
$: in each round, one edge is activated uniformly and independently at random and (only) its …

We prove a local law and eigenvector delocalization for general Wigner-type matrices. Our
methods allow us to get the best possible interval length and optimal eigenvector …

We outline some recent proofs of quantum ergodicity on large graphs and give new
applications in the context of irregular graphs. We also discuss some remaining questions …