Monotonicity conjecture for Gaussian noise stability at fixed volume
For a∈(0,1)a\in(0,1)a∈(0,1), let J(a,a;ρ)J(a,a;\rho)J(a,a;ρ) denote the Gaussian noise-stability quantity for two sets of Gaussian measure aaa, and let EρJ(1A(X),1A(Y);ρ)\mathbb{E}_\rho J(1_A(X),1_A(Y);\rho)EρJ(1A(X),1A(Y);ρ) denote the cor…