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math.CO2024
When do the Kahn-Kalai Bounds Provide Nontrivial Information?
Bryce Alan Christopherson, Jack Baretz
The Park-Pham theorem (previously known as the Kahn-Kalai conjecture), bounds the critical probability, , of the a non-trivial property …
math.CO2024
Conditional Park--Pham Bounds under Positive Correlation
Bryce Alan Christopherson, Darian Colgrove
We record a conditional form of the -dependent Park--Pham theorem. If a monotone property is positively correlated with a conditioning event $B\subset…