The time marginal of the boundary potential

The public Stieltjes clock inherits the normalized mean potential of the auxiliary clock.

theorem BGW.StableTrees.lintegral_supBoundaryPotential_zero_right {θ : ℝ} (hθ : 1 < θ ∧ θ ≤ 2) {q : ℝ} (hq : 0 < q) : ∫⁻ (f : Skorokhod.DLoc), supBoundaryPotential θ q 0 f ∂↑(stableLocalLaw θ) = ENNReal.ofReal (q ^ (1 / θ) / q)

Zero-order case λ = 0: E ∫_0^∞ e^{-qt} dM_t = Φ/q = q^{1/θ - 1} (= 1 at q = 1).