The lazy hit-and-run walk mixes from an M-warm start on any isotropic convex body in O(n^2 ψ_n^{-2} log^3(M/ε)) total-variation distance, matching the ball walk up to logarithmic factors.
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Hit-and-Run Mixes as Fast as the Ball Walk
The lazy hit-and-run walk mixes from an M-warm start on any isotropic convex body in O(n^2 ψ_n^{-2} log^3(M/ε)) total-variation distance, matching the ball walk up to logarithmic factors.