18 papers
Distinguishability threshold for random geometric graphs
Zach Hunter, Aleksa MilojeviÄ, Benny Sudakov
The spherical random geometric graph is obtained by sampling independent points uniformly on the unit sphere and joining pair…
Gilbreath's conjecture: a Cramér random model and a deterministic analysis
Zachary Chase, Zach Hunter, Terence Tao
Gilbreath's conjecture asserts that if one starts with the sequence of primes and takes successive absolute differences to create a triangular array, then the left diagonal of this…
Nearly tight bounds for induced subdivisions
Zach Hunter, Aleksa MilojeviÄ, Patryk Morawski +1
Subdivisions of complete graphs play a central role in combinatorics, having deep connections to structural, extremal, and topological aspects of graph theory. A celebrated conject…
Three-color van der Waerden numbers grow super-exponentially
Jacob Fox, Zach Hunter
For sufficiently large, we show that there is a three-coloring of the first positive integers without any monochromatic -term arithmetic progressions. T…
Gaussian random graphs and Ramsey numbers
Zach Hunter, Aleksa MilojeviÄ, Benny Sudakov
We give a simple proof of the recent remarkable exponential improvement for Ramsey lower bounds, obtained by Ma, Shen and Xie. Our key ingredient is an alternative construction bas…
Communication Complexity of Disjointness under Product Distributions
Zach Hunter, Aleksa MilojeviÄ, Benny Sudakov +1
Determining the randomized (or distributional) communication complexity of disjointness is a central problem in communication complexity, having roots in the foundational work of B…