Rates of Convergence for 'Features' of a Markov Chain
summary
Shows that many natural features mix far faster than global distance: simple walk on Z_p mixes a half-circle feature in p squared steps but parity in O(1); riffle shuffle has cutoff at 3/2 log2 n in total variation, yet red/black needs ~log2 n, top-card ~1/2 log n, LIS ~5/6 log2 n, and certain bridge dealing orders improve separation by a factor of 10. Proves a general separation formula for types Di≥3, uses local limit theorems and higher Fourier (Green–Tao) methods, and proves in U3(p) the central coordinate mixes in p steps while full group needs p squared, leaving abstraction questions.
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