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Concentration of Lipschitz Functionals of Determinantal and Other Strong Rayleigh Measures

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Proves that homogeneous measures with the stochastic covering property (including strong Rayleigh/determinantal and balanced matroid laws such as uniform spanning trees) satisfy a 1‑Lipschitz concentration bound P{|F−E F|>a} ≤ exp(−a^2/(8K)), using a K‑step Doob martingale from a sequential K‑sampling procedure plus a coupling that shifts conditioned laws by one bit. Extends to non‑homogeneous strong Rayleigh laws with a weaker bound exp(−3e a^2/(16a+2μ)).

AI-written summary · about

  1. 0:00Introduction
  2. 3:20Example
  3. 10:15Covering Property
  4. 26:45Other Examples
  5. 30:10Proof
  6. 33:58Homogeneous Theorem
  7. 42:16Martingale
  8. 45:34Rayleigh Property
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