Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 6 of 6 for “"Conformal welding"”.
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The Beurling-Ahlfors extension and Conformal welding
This thesis introduces the theory of conformal welding and shows that every quasisymmetric function is a welding homeomorphism. Conformal weldings appear naturally in Teichmüller theory when we consider the conditions under which two Riemann surfaces can be joined together. In the second chapter we …
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Conformal welding of random surfaces from Liouville theory
… scaling limit for random planar maps. Liouville conformal field theory (LCFT) 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 …
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Fine regularity properties of SLE_4 and SLE_8
… also show that the Jones-Smirnov condition for conformal removability (with quasi hyperbolic geodesics) does not hold for SLE$_{4}$. In addition to the above results, we show that the modulus of continuity for SLE$_{8}$ with the capacity parameterization is given by (log($\delta$$^{-1}$))$^{-1/4 …
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Random conformally covariant metrics in the plane
This thesis is in the broad area of random conformal geometry, combining tools from probability and complex analysis. We mainly consider *Liouville quantum gravity* (LQG), a model introduced in the physics literature in the 1980s by Polyakov in order to provide a canonical example of a random …
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Integrability in random conformal geometry
… in many statistical physics models. Liouville conformal field theory (LCFT) is the quantum field theory underlying LQG. Each of these satisfies conformal invariance or covariance. This thesis proves exact formulas in random conformal geometry; we highlight a few here. The Brownian annulus …
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On Gaussian multiplicative chaos and conformal field theory
This thesis is concerned with conformally invariant stochastic processes in two dimensions and their applications to conformal field theory (CFT). The main probabilistic objects are the Gaussian free field (GFF) and the random geometries associated to it. Especially, we are interested in Gaussian …