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Showing 1 to 10 of 10 for “"Schramm Loewner evolution"”.
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Gaussian free field, Schramm-Loewner evolution and Liouville quantum gravity
Consider an instance h of the Gaussian free field on a simply connected domain ... We study several properties of the level lines: continuity, monotonicity, reversibility and target-independence ... In the second part, we study Liouville quantum gravity(LQG).
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Conformal loop ensembles and the Gaussian free field
… objects, such as the Gaussian free field, the Schramm-Loewner evolution, and the conformal loop ensemble. Just as Brownian motion is a scaling limit of discrete random walks, these objects serve as universal scaling limits of functions or paths associated with the underlying discrete models. We …
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Random conformally covariant metrics in the plane
… to get another LQG surface decorated by a *Schramm--Loewner evolution* (SLE) curve, the LQG metric on the resulting surface can be obtained as a natural metric space quotient of those on the two original surfaces. This generalizes results of Gwynne and Miller in the special case $\gamma = …
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Integrability in random conformal geometry
… as the scaling limit of random planar maps. Schramm-Loewner evolution (SLE) is a random planar curve describing the scaling limits of interfaces in many statistical physics models. Liouville conformal field theory (LCFT) is the quantum field theory underlying LQG. Each of these satisfies …
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Cardy embedding of random planar maps and a KPZ formula for mated trees
The Schramm-Loewner evolution (SLE) is a random fractal curve which describes the scaling limit of interfaces in a wide range of statistical physics models. Liouville quantum gravity (LQG) is a random fractal surface which arises as the scaling limit of discrete surfaces known as random planar maps …
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Conformal welding of random surfaces from Liouville theory
… is the underlying 2D CFT that governs LQG. Schramm-Loewner evolution (SLE) is a random planar curve, which describes the scaling limits of interfaces in many statistical physics models. As discovered by Sheffield (2010), one of the deepest results in random geometry is that SLE curves arises …
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Continuum Methods and Tightness Results for Non-Simple SLE and CLE: Existence, Interactions, and Metric Approximations
This thesis presents results in the theory of Schramm-Loewner Evolution (SLE) and Conformal Loop Ensembles (CLE), which are random fractal structures describing scaling limits of interfaces in two-dimensional statistical physics models. In particular, we deal with the construction and interaction …
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Fine regularity properties of SLE_4 and SLE_8
The Schramm-Loewner evolution (SLE$_{\kappa}$) is a one parameter family ($\kappa$>0) of curves which connect two boundary points of a simply connected domain. It was introduced by Schramm in 1999 as a candidate to describe the scaling limits of the interfaces in statistical mechanics models on …
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Exploring Random Geometry with the Gaussian Free Field
… the continuum. Chapter 1 is an introduction to Schramm-Loewner evolutions (SLE). SLEs are the canonical family of non-self-intersecting, conformally invariant random curves with a domain-Markov property. The family is indexed by a parameter, usually denoted by κ, which controls the regularity of …
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On Gaussian multiplicative chaos and conformal field theory
… in Gaussian multiplicative chaos (GMC), Schramm-Loewner evolution (SLE) and Liouville CFT, which can be understood as theories of random surfaces. From the point of view of physics, the idea of a ``summing over surfaces" can be traced back to Polyakov's work on bosonic string theory. …