1 research outputs found
Hypercontractive inequalities via SOS, and the Frankl--R\"odl graph
Our main result is a formulation and proof of the reverse hypercontractive
inequality in the sum-of-squares (SOS) proof system. As a consequence we show
that for any constant , the SOS/Lasserre SDP hierarchy at
degree certifies the statement "the maximum
independent set in the Frankl--R\"odl graph has
fractional size~". Here is the graph
with and whenever (an
even integer). In particular, we show the degree- SOS algorithm certifies
the chromatic number lower bound "",
even though is the canonical integrality gap instance
for which standard SDP relaxations cannot even certify
"". Finally, we also give an SOS proof of (a
generalization of) the sharp -hypercontractive inequality for any even
integer