Existence and uniqueness of a canonical Brownian motion on CLE_κ gaskets for κ ∈ (4,8), characterized by a unique locally determined resistance form satisfying invariance properties.
Resistance forms, quasisymmetric maps and heat kernel estimates
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Proves scale-invariant boundary Harnack principle on uniform domains under scale-invariant elliptic Harnack inequality without geodesic assumption or a priori Green functions.
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Existence and uniqueness of the canonical Brownian motion in non-simple conformal loop ensemble gaskets
Existence and uniqueness of a canonical Brownian motion on CLE_κ gaskets for κ ∈ (4,8), characterized by a unique locally determined resistance form satisfying invariance properties.
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Boundary Harnack principle on uniform domains
Proves scale-invariant boundary Harnack principle on uniform domains under scale-invariant elliptic Harnack inequality without geodesic assumption or a priori Green functions.