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a89d282 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | import OAI.Probability.InvariantIsing.Core.InvariantOrbitLaw
import OAI.Probability.InvariantIsing.Pressure.RandomOrbitLaw
namespace OAI
/-! Fixed-data sections of the physical pressure and right-Haar transport. -/
noncomputable section
open MeasureTheory
namespace InvariantIsing
lemma measurable_dataPhysicalPressure_section {N : ℕ} (hN : 0 < N)
(d : FieldSpectralData N) : Measurable (dataPhysicalPressure d) := by
exact Measurable.of_uncurry_left (f := dataPhysicalPressure) (x := d)
(measurable_dataPhysicalPressure hN)
lemma physical_orbit_kernel {N : ℕ} (hN : 0 < N)
(H : Measure (Orthogonal N)) [H.IsMulRightInvariant]
(d : FieldSpectralData N) (Y : Orthogonal N → ℝ) (V : Orthogonal N)
(hY : ∀ U, Y U=dataPhysicalPressure d (U*V)) :
H.map (fun U => (d,Y U))=H.map (fun U => (d,dataPhysicalPressure d U)) := by
exact paired_map_eq_of_comp H d (dataPhysicalPressure d) Y (fun U => U*V)
(measurable_dataPhysicalPressure_section hN d) (measurable_id.mul_const V)
(map_mul_right_eq_self H V) hY
end InvariantIsing
end
end OAI
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