114 citations · 1k across the 63 of their papers we have counts for
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An theory of sparse graph convergence II: LD convergence, quotients, and right convergence
Christian Borgs, Jennifer T. Chayes, Henry Cohn +1
We extend the theory of sparse graph limits, which was introduced in a companion paper, by analyzing different notions of convergence. Under suitable restrictions on node wei…
The Green-Tao theorem: an exposition
David Conlon, Jacob Fox, Yufei Zhao
The celebrated Green-Tao theorem states that the prime numbers contain arbitrarily long arithmetic progressions. We give an exposition of the proof, incorporating several simplific…
On the variational problem for upper tails in sparse random graphs
Eyal Lubetzky, Yufei Zhao
What is the probability that the number of triangles in , the Erdős-Rényi random graph with edge density , is at least twice its mean? Writing it as $\exp[- r…
An theory of sparse graph convergence I: limits, sparse random graph models, and power law distributions
Christian Borgs, Jennifer T. Chayes, Henry Cohn +1
We introduce and develop a theory of limits for sequences of sparse graphs based on graphons, which generalizes both the existing theory of dense graph limits and…