N lim 1( 1: f(nkx)) = 0, N-N k_l or roughly speaking the strong law of large numbers holds for f(nkx) (in fact the authors prove that Ef(nkx)/k converges almost everywhere) . The question was raised… Expand

The problem of identifying a planted assignment given a random k-SAT formula consistent with the assignment exhibits a large algorithmic gap: while the planted solution can always be identified given a formula with O(n log n) clauses.Expand

We consider a bipartite stochastic block model on vertex sets $ V_1$ and $V_2$, with planted partitions in each, and ask at what densities efficient algorithms can recover the partition of the smaller vertex set.Expand

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems (CSP), via a common generalization in terms of random bipartite graphs.Expand

We give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model in the non-uniqueness regime of the infinite $\Delta$-regular tree.Expand

We prove a lower bound of $\Omega (d^{3/2} \cdot (2/\sqrt{3})^d)$ on the kissing number in dimension $d$. This improves the classical lower bound of Chabauty, Shannon, and Wyner by a linear factor in… Expand

We present several new results on the phase transition of the Bohman-Frieze random graph process, a simple modification of the Erd\H{o}s-R\'{e}nyi process.Expand

We prove an asymptotically tight lower bound on the average size of independent sets in a triangle-free graph on $n$ vertices with maximum degree $d$, showing that an independent set drawn uniformly… Expand

We prove tight upper bounds on the logarithmic derivative of the independence and matching polynomials of d-regular graphs and prove the asymptotic upper matching conjecture of Friedland, Krop, Lundow, and Markstrom.Expand