Kivonat: The Erdos-Simonovits-Sidorenko conjecture is well-known in combinatorics but it has equivalent formulations in analysis and probability theory. The shortest formulation is an integral inequality related to Mayer integrals in statistical mechanics and Feynman integrals in quantum field theory. We present new progress in the area using couplings of probability spaces and entropy calculations.

Part of the talk is based on joint results with J.L. Xiang Li.