OAI/Combinatorics/ContingencyTables/Sampling/AllSmallChain.lean

GitHub source file

8 declarations, 0 contain sorry, 0 declared as axioms

The small-state walk when no dense completion remains

Every retained completion then has weight one. The same local graph is sampled by accepting every valid proposal; no reference row is chosen.

  1. def OAI.ContingencyTables.SmallGraphProfiles.unitSmallChain line 26
  2. lemma OAI.ContingencyTables.SmallGraphProfiles.unitSmallChain_pi line 34
  3. lemma OAI.ContingencyTables.SmallGraphProfiles.unitSmallChain_energy line 39
  4. lemma OAI.ContingencyTables.SmallGraphProfiles.stateGraphEnergy_allSmall line 51
  5. lemma OAI.ContingencyTables.SmallGraphProfiles.allowance_fourteen line 60
  6. lemma OAI.ContingencyTables.SmallGraphProfiles.unitSmallChain_pi_weight line 66
  7. lemma OAI.ContingencyTables.SmallGraphProfiles.unitSmallChain_energy_lower line 72
  8. theorem OAI.ContingencyTables.SmallGraphProfiles.unitSmallChain_poincare line 88

    Source documentation

    The full graph bound includes the empty large rectangle.

    theorem unitSmallChain_poincare [Nonempty I] [Nonempty J]
    (hsmall : ∀ i j,FirstPaperPhysicalMarginal.paperSmall r c i j=true)
    (H : PaperStates r c → ℝ) :
    (unitSmallChain r c).variance H ≤ (d:ℝ)^160*(unitSmallChain r c).energy H := by
…

    Mentions: OAI.ContingencyTables.FirstPaperPhysicalMarginal.paperSmall, OAI.ContingencyTables.SmallGraphProfiles.PaperStates, OAI.ContingencyTables.SmallGraphProfiles.unitSmallChain