Sharp Lovasz-Theta Bounds on Random Graphs

It is well known that the \Lovasz-Theta function of a random graph $G(n,\tfrac{1}{2})$ is $Θ(\sqrt{n})$. More precisely, it is tightly concentrated in the interval \( [\sqrt{n},\, 2\sqrt{n}], \) where the upper bound follows from an explicit dual witness for the associated semidefinite program. Nume