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We will discuss and study several models of random geometry - these are probabilistic models of random curves, surfaces, metrics often stemming from statistical physics and or field theories. ...
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 ...
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 ...
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 ...