Coordinate-flip generator on a hypercube
= Coordinate-flip generator on a hypercube
{title2=$Lf(\omega)=\tfrac12\sum_i(f(\omega^{(i)})-f(\omega))$}
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 $-\mathbb E[fLf]=\frac14\sum_i\mathbb E(f(\omega^{(i)})-f(\omega))^2$.