The SDP value of random 2CSPs

We consider a very wide class of models for sparse random Boolean 2CSPs; equivalently, degree-2 optimization problems over {±1}. For each modelM, we identify the “high-probability value” sM of the natural SDP relaxation (equivalently, the quantum value). That is, for all > 0 we show that the SDP optimum of a random n-variable instance is (when normalized by n) in the range (sM− , sM+ ) with high probability. Our class of models includes non-regular CSPs, and ones where the SDP relaxation value is strictly smaller than the spectral relaxation value.

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