When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

We explore the asymptotic properties of strategic models of network formation in very large populations. Specifically, we focus on (undirected) exponential random graph models. We want to recover a ...

For any α ∈ (0, 1) and any nα ≤ d ≤ n/2, we show that λ(G) ≤ Cα√d with probability at least 1− 1 n , where G is the uniform random undirected d-regular graph on n vertices, λ(G) denotes its second ...