OAI/Probability/InvariantIsing/Cavity/CavityFiniteCovariance.lean

GitHub source file

10 declarations, 0 contain sorry, 0 declared as axioms

Positivity and precision of the finite-alphabet covariance used by the cavity calculation. No dimension-dependent spectral bound is needed.

  1. def OAI.InvariantIsing.cavityFiniteCovariance line 16
  2. lemma OAI.InvariantIsing.cavityFiniteCovariance_diagonal line 20
  3. lemma OAI.InvariantIsing.cavityFiniteCovariance_posDef line 36
  4. lemma OAI.InvariantIsing.cavityFiniteCovariance_sub_posSemidef line 43
  5. lemma OAI.InvariantIsing.finiteInverse_strict_antitone_pos line 57
  6. lemma OAI.InvariantIsing.cavityFiniteCovariance_sub_posDef line 68
  7. lemma OAI.InvariantIsing.cavityFiniteCovariance_root_posSemidef line 82
  8. theorem OAI.InvariantIsing.cavityFiniteCovariance_step_precision line 95
  9. theorem OAI.InvariantIsing.cavityFiniteCovariance_terminal_precision line 130
  10. lemma OAI.InvariantIsing.cavity_finite_spectral_upper line 145