| import OAI.Analysis.IrrationalRotation.Model.BlockedProductCoupling |
| import OAI.Analysis.IrrationalRotation.Model.ProductScales |
| import OAI.Analysis.IrrationalRotation.Model.ProductCocycle |
| import OAI.Analysis.IrrationalRotation.Model.SourceCouplingMarginals |
|
|
| namespace OAI |
|
|
| noncomputable section |
| open scoped ComplexConjugate |
|
|
| namespace Invariant233.BlockedProductCoupling |
|
|
| def sourceBasisZero : ProductModel.Fiber := lp.single 2 (0 : ℤ) (1 : ℂ) |
|
|
| abbrev ProjectionField := ProductModel.Base → ProductModel.Fiber →L[ℂ] ProductModel.Fiber |
|
|
| def projectionDiagonal (P : ProjectionField) (x : ProductModel.Base) : ℝ := |
| ((P x sourceBasisZero) 0).re |
|
|
| def sourceRetainedEvent {X : Type*} (m : ℕ → ℕ) (K : ℕ → ℝ) |
| (r : X → ℝ) (x y : Sample m → X) (j : ℕ) : Set (Sample m) := |
| currentEvent m j \ (futureBad m K j ∪ |
| ({z | r (x z) < 1 / ((j + 1 : ℕ) : ℝ)} ∪ |
| {z | 1 - r (y z) < 1 / ((j + 1 : ℕ) : ℝ)})) |
|
|
| noncomputable def sourceLaw (p : ProductScaleData) (j : ℕ) : MeasureTheory.Measure (Sample p.m) := |
| law p.m ProductScaleData.kappa (fun s _ => p.a s) (fun s _ => p.b s) j |
|
|
| def sourceEvent (p : ProductScaleData) (e : ℕ ≃ Σ s, Fin (p.m s)) |
| (r : ProductModel.Base → ℝ) (j : ℕ) : Set (Sample p.m) := |
| sourceRetainedEvent p.m (fun s => (p.K s : ℝ)) r |
| (circleLeftEndpoint e) (circleRightEndpoint e) j |
|
|
| def unflatten {m : ℕ → ℕ} (e : ℕ ≃ Σ s, Fin (m s)) |
| (ω : OrderedProductCoupling.Sample) : Sample m := |
| fun s i => ω (e.symm ⟨s, i⟩) |
|
|
| def flatSourceEvent (p : ProductScaleData) (e : ℕ ≃ Σ s, Fin (p.m s)) |
| (r : ProductModel.Base → ℝ) (j : ℕ) : Set OrderedProductCoupling.Sample := |
| unflatten e ⁻¹' sourceEvent p e r j |
|
|
| def sourceCoefficientA (p : ProductScaleData) (e : ℕ ≃ Σ s, Fin (p.m s)) |
| (θ : ℕ → ℝ) (P : ProjectionField) (z : Sample p.m) (v : ℤ) : ℂ := |
| (P (circleLeftEndpoint e z) sourceBasisZero) v / |
| (ProductCocycle.cocycleVersion θ (fun i => p.C (e i).1) v |
| (circleLeftEndpoint e z) : ℂ) |
|
|
| def sourceCoefficientB (p : ProductScaleData) (e : ℕ ≃ Σ s, Fin (p.m s)) |
| (θ : ℕ → ℝ) (P : ProjectionField) (z : Sample p.m) (v : ℤ) : ℂ := |
| (ProductCocycle.cocycleVersion θ (fun i => p.C (e i).1) (-v) |
| (circleRightEndpoint e z) : ℂ) * |
| conj (((1 - P (circleRightEndpoint e z)) sourceBasisZero) (-v)) |
|
|
| end Invariant233.BlockedProductCoupling |
|
|
| end |
|
|
| end OAI |
|
|
