OAI/Combinatorics/ContingencyTables/Dense/DenseMixing.lean

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8 declarations, 0 contain sorry, 0 declared as axioms

Numerical Poincaré and point mixing for the dense bin sampler

  1. theorem OAI.ContingencyTables.GridBoundary.denseCutConstant_lower line 14
  2. theorem OAI.ContingencyTables.GridBoundary.densePoincareConstant_upper line 24
  3. theorem OAI.ContingencyTables.GridBoundary.dense_min_mass_exponential line 39
  4. theorem OAI.ContingencyTables.GridBoundary.dense_mixing_time_arithmetic line 72
  5. theorem OAI.ContingencyTables.GridBoundary.denseBinChain_polynomial_poincare line 117
  6. theorem OAI.ContingencyTables.GridBoundary.denseBinChain_point_mixing line 132
  7. theorem OAI.ContingencyTables.GridBoundary.denseBinChain_relative_mixing line 153
  8. theorem OAI.ContingencyTables.GridBoundary.denseBinChain_total_variation line 174

    Source documentation

    Total variation for the actual law, written as its density against the proved stationary distribution. The pointwise relative bound is stronger than the manuscript's total-variation conclusion.

    theorem denseBinChain_total_variation (R : Option I → ℕ) (P : Option J → ℕ)
    (d : ℕ) (hd : 14 ≤ d) (hR : ∀ i, d ^ 12 ≤ R i) (hP : ∀ j, d ^ 12 ≤ P j)
    (hRmax : ∀ i, R (some i) ≤ R none) (hPmax : ∀ j, P (some j) ≤ P none)
    (hdimR : Fintype.card (Option I) ≤ d) (hdimP : Fintype.card (Option J) ≤ d)
    (hfree : Fintype.card (I × J) ≤ d) (htotal : ∑ i, R i = ∑ j, P j)
    (e : I × J ≃ Fin q) (hPL : PublishedInputs.FiniteBoxPrekopaLeindler q)
    (hCheeger : PublishedInputs.FiniteCheeger (Grid (I := Fin q) (4 * d ^ 8)))
…

    Mentions: OAI.ContingencyTables.PublishedInputs.FiniteBoxPrekopaLeindler, OAI.ContingencyTables.PublishedInputs.FiniteCheeger, OAI.ContingencyTables.GridBoundary.Grid