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math.PR2024★ 1 cited
Lower tails for triangles inside the critical window
Matthew Jenssen, Will Perkins, Aditya Potukuchi +1
We study the probability that the random graph is triangle-free. When or the asymptotics of the logarithm of this probability are known…
cs.DS2024
Sampling and counting triangle-free graphs near the critical density
Matthew Jenssen, Will Perkins, Aditya Potukuchi +1
We study the following combinatorial counting and sampling problems: can we efficiently sample from the Erdős-Rényi random graph conditioned on triangle-freeness? Can we e…
math.CO2024
Searching for (sharp) thresholds in random structures: where are we now?
Will Perkins
We survey the current state of affairs in the study of thresholds and sharp thresholds in random structures on the occasion of the recent proof of the Kahn--Kalai Conjecture by Par…