OAI/Probability/InvariantIsing/Magnetic/MagneticOffDiagonalHessian.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

The mixed sign of the constrained height Hessian follows from the actual positive coordinate variation. Together with radial monotonicity, it gives the negative quadratic-form sign.

  1. lemma OAI.InvariantIsing.deriv_nonpos_of_right_order line 17
  2. lemma OAI.InvariantIsing.update_eq_coordinate_line line 24
  3. lemma OAI.InvariantIsing.heightLevel_update line 34
  4. lemma OAI.InvariantIsing.magneticHeightLevel_coordinate_right_order line 45
  5. theorem OAI.InvariantIsing.magneticHeightSchur_mixed_nonneg line 82
  6. theorem OAI.InvariantIsing.magneticHeightSchur_quadratic_nonpos line 105