StreamIncrementLpLargeCube #
Ported from scottnarmstrong/Superdiffusion at 7f20476385d4af418f110303085ad0740c9eba46. Module imports, support namespace and local option directives adapted for Lean Pool.
theorem
Algsuperdiff.Frozen.Section3.stream_increment_lp_large_cube_bound
(d : ℕ)
:
∃ (C : ℝ),
0 < C ∧ ∀ (M : Section3.ABKModel d) (p : ℝ),
1 ≤ p →
∀ (l m n : ℤ),
n < m →
m ≤ l →
Section3.Probability.IsDeterministicShiftOneSidedOrlicz (↑M.P)
(HCPolySupport.IndependentSums.gammaSigma (2 / p))
(Section3.Provider.Stream.streamIncrementLpMass p l n m)
((C * p) ^ (p / 2) * (min M.gamma⁻¹ (↑m - ↑n) * 3 ^ (2 * M.gamma * ↑m)) ^ (p / 2))
((C * p) ^ (p / 2) * (min M.gamma⁻¹ (↑m - ↑n) * 3 ^ (2 * M.gamma * ↑m)) ^ (p / 2) * 3 ^ (-(↑d / 2) * (↑l - ↑m)))