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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For κ in K (where the adjacency graph of SLE_κ complementary components is a.s. connected), the range of SLE_κ is a.s. conformally removable; a conformally covariant measure on cut points is constructed as an intermediate step.
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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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Conformal removability of non-simple Schramm-Loewner evolutions
For κ in K (where the adjacency graph of SLE_κ complementary components is a.s. connected), the range of SLE_κ is a.s. conformally removable; a conformally covariant measure on cut points is constructed as an intermediate step.