 Coordinate-flip generator on a hypercube

For independent coordinate flips at rate $1/2$, a Walsh character $w_A$ is an eigenfunction with eigenvalue $-|A|$. The generator is self-adjoint and negative semidefinite. Its Dirichlet form of a Markov chain is $-\mathbb{E}[fLf]=\frac{1}{4}{\sum }_i\mathbb{E}(f({\omega }^{(i)})-f(\omega ){)}^2$.