منابع مشابه
Imaginary Geometry I: Interacting SLEs
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...
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We present basic properties of Dipolar SLEs, a new version of stochastic Loewner evolutions (SLE) in which the critical interfaces end randomly on an interval of the boundary of a planar domain. We present a general argument explaining why correlation functions of models of statistical mechanics are expected to be martingales and we give a relation between dipolar SLEs and CFTs. We compute SLE ...
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The invention of non-Euclidean geometries is often seen through the optics of Hilbertian formal axiomatic method developed later in the 19th century. However such an anachronistic approach fails to provide a sound reading of Lobachevsky’s geometrical works. Although the modern notion of model of a given theory has a counterpart in Lobachevsky’s writings its role in Lobachevsky’s geometrical the...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2016
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-016-0698-0