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Our motivation in this paper is twofold. First, we study the geometry of a class of exploration sets, called exit sets, which are naturally associated with a 2D vector-valued Gaussian Free Field: ϕ:Z2→RN, N≥1. W ...
In this note we continue the study of imaginary multiplicative chaos µβ:= exp(iβΓ), where Γ is a two-dimensional continuum Gaussian free field. We concentrate here on the fine-scale analytic properties of |µβ (Q(x, r))| as r → 0, where Q(x, r) is a square ...
Consider a log-correlated Gaussian field Γ and its associated imaginary multiplicative chaos: eiβΓ: where β is a real parameter. In [3], we showed that for any nonzero test function f, the law of∫ f: eiβΓ: possesses a smooth density with respect to Lebesgu ...
