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math.PR2024
Upper tails for arithmetic progressions revisited
Matan Harel, Frank Mousset, Wojciech Samotij
Let be the number of -term arithmetic progressions contained in the -biased random subset of the first positive integers. We give asymptotically sharp estimates on th…
math.CO2024
Stability of large cuts in random graphs
Ilay Hoshen, Wojciech Samotij, Maksim Zhukovskii
We prove that the family of largest cuts in the binomial random graph exhibits the following stability property: If , then, with high probability, there is a se…