OAI/Probability/SLE/Multipoint/MultipointYoung.lean
4 declarations, 0 contain sorry, 0 declared as axioms
Weighted Young absorption for the pair terms in the multipoint regularized product. The constant depends on the order and SLE parameter, not the two target levels or their current clocks.
- def
OAI.SLEExactGauge.Multipoint.youngConstantline 12 - lemma
OAI.SLEExactGauge.Multipoint.youngConstant_posline 15 - lemma
OAI.SLEExactGauge.Multipoint.three_factor_youngline 22 - theorem
OAI.SLEExactGauge.Multipoint.weighted_pair_absorptionline 63Source documentation
The factor from the singular angular derivatives is absorbed with coefficient ε at both vertices and a deterministic inverse-regulator cost.
theorem weighted_pair_absorption {p C ε D x y z : ℝ} (hp : 0 < p) (hC : 0 < C) (hε : 0 < ε) (hD : 0 < D) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : C*D^(-1-eta p)*x^(eta p)*y^(eta p)*z^(1-2*eta p) ≤ ε*(x+y) + youngConstant p C ε*D^(-exponent p)*z := by …Mentions: OAI.SLEExactGauge.Multipoint.eta, OAI.SLEExactGauge.Multipoint.youngConstant, OAI.SLEExactGauge.Multipoint.exponent