Fix constants χ > 0 and θ ∈ [0, 2π), and let h be an instance of the Gaussian free field on a planar domain. We study flow lines of the vector field ei(h/χ+θ) starting at a fixed boundary point of the domain. Letting θ vary, one obtains a family of curves that look locally like SLEκ processes with κ ∈ (0, 4) (where χ = 2 √ κ − √ κ 2 ), which we interpret as the rays of a random geometry with pu...

In this paper we introduce the notion of a discrete-time negative imaginary system and we investigate its relations with discrete-time positive real system theory. In the framework presented here, discrete-time negative imaginary systems are defined in terms of a sign condition that must be satisfied in a domain of analyticity of the transfer function, in analogy with the case of discrete-time ...

We prove that a countable simple unidimensional theory that eliminates hyperimaginaries is supersimple. This solves a problem of Shelah in the more general context of simple theories under weak assumptions.