Introduction to Analysis on the Discrete Cube II
summary
Shows that two constructions of the continuous-time random walk on the discrete cube — the lazy discrete-time walk rescaled and independent coordinate Poisson flips — produce the same semigroup because they agree on the Walsh basis, with Walsh functions as eigenfunctions and the generator multiplying each Walsh by |S|. Writes L = (n/2)I − K, proves symmetry with respect to the uniform measure, contractivity on Lp, and defines the Dirichlet energy E(f)=⟨f,Lf⟩ = 1/2 sum_{edges}(f(x)−f(y))^2. Gives the Poissonization argument that creates coordinate independence.
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