Antoine Jego, Universite Paris Dauphina, France, Titus Lupu, Sorbonne Universite, Paris, France, and Wei Qian, The University of Hong Kong, People's Republic of China

• Chapters1. Introduction and main results2. Preliminaries3. Convergence of renormalised crossing probabilities and coupling of clusters4. Construction of $h_\theta $: Proof of Theorems , and5. $h_\theta $ as a sum of Minkowski measures: Proof of Theorems and6. Excursions from the boundary of a cluster7. Properties of $h_\theta $ and height gap8. Approximation of $\mathcal {M}_a^ $ from the discrete9. Wick powers and expansion of $\mathcal {M}_a^ $

Antoine Jego, Universite Paris Dauphina, France, Titus Lupu, Sorbonne Universite, Paris, France, and Wei Qian, The University of Hong Kong, People's Republic of China

• Chapters1. Introduction and main results2. Preliminaries3. Convergence of renormalised crossing probabilities and coupling of clusters4. Construction of $h_\theta $: Proof of Theorems , and5. $h_\theta $ as a sum of Minkowski measures: Proof of Theorems and6. Excursions from the boundary of a cluster7. Properties of $h_\theta $ and height gap8. Approximation of $\mathcal {M}_a^ $ from the discrete9. Wick powers and expansion of $\mathcal {M}_a^ $

Antoine Jego, Universite Paris Dauphina, France, Titus Lupu, Sorbonne Universite, Paris, France, and Wei Qian, The University of Hong Kong, People's Republic of China

• Chapters1. Introduction and main results2. Preliminaries3. Convergence of renormalised crossing probabilities and coupling of clusters4. Construction of $h_\theta $: Proof of Theorems , and5. $h_\theta $ as a sum of Minkowski measures: Proof of Theorems and6. Excursions from the boundary of a cluster7. Properties of $h_\theta $ and height gap8. Approximation of $\mathcal {M}_a^ $ from the discrete9. Wick powers and expansion of $\mathcal {M}_a^ $