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 12 of 12 for “"Liouville quantum gravity"”.
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Frontiers of Liouville quantum gravity
… of random geometry in two dimensions called Liouville quantum gravity (LQG). LQG was originally described heuristically by physicists, and mathematicians have grappled with the challenge of defining it rigorously and analyzing its properties. We investigate elements of the theory of LQG that …
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Gaussian free field, Schramm-Loewner evolution and Liouville quantum gravity
… ... In the second part, we study Liouville quantum gravity(LQG).
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Random surface interpretations of two-dimensional Liouville quantum gravity and Yang-Mills theory
… over surfaces") has its historical roots in quantum gravity, string theory, statistical physics, and combinatorics. This thesis explores random surfaces in two settings: one related to Liouville quantum gravity, and one related to Euclidean Yang-Mills theory in two dimensions. The first part …
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On the metric structure of random planar maps and SLE-decorated Liouville quantum gravity
… of random fractal surfaces called [gamma]-Liouville quantum gravity (LQG) surfaces with parameter [gamma] E (0, 2]. We study the large-scale structure of random planar maps (and statistical mechanics models on them) viewed as metric measure spaces equipped with the graph distance and the …
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Scaling limit of critical systems in random geometry
… evolutions, the Gaussian free field, Liouville quantum gravity and the Brownian continuum random tree. We begin by considering branching diffusions in a bounded domain $D\subset$ $R^{d}$, in which particles are killed upon hitting the boundary $\partial D$. It is known that such a …
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Matings of negatively correlated trees with applications to Schnyder woods and bipolar orientations
… thesis, we study the mating of trees approach to Liouville quantum gravity decorated with SLE curves and its application to the scaling limit theory of decorated random planar maps. We focus on the less investigated regime where the SLE parameter K is larger than 8. We obtain three main results. …
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Fine regularity properties of SLE_4 and SLE_8
… connections to the Gaussian free field (GFF) and Liouville quantum gravity (LQG). The first part of the thesis treats the values $\kappa$ = 4 and $\kappa$ = 8. The value $\kappa$ = 4 is special because it is the critical value at or below which SLE$_{\kappa}$ curves are simple and above which they …
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Random conformally covariant metrics in the plane
… 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 surface with conformal symmetries and formally given by the Riemannian metric tensor …
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Integrability in random conformal geometry
Liouville quantum gravity (LQG) is a random surface arising 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 …
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Exploring Random Geometry with the Gaussian Free Field
… We also look at how the GFF is used to define Liouville quantum gravity (LQG) surfaces, and how thick points of the GFF relate to the quantum gravity measure. Chapter 3 introduces a diffusion on LQG surfaces, the Liouville Brownian motion (LBM). The main goal of the chapter is to complete an …
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Cardy embedding of random planar maps and a KPZ formula for mated trees
… 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 (RPM). First, we study Hausdorff dimensions for SLE curves. We prove a KPZ-type formula which relates the …
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Conformal welding of random surfaces from Liouville theory
Liouville quantum gravity (LQG) is a natural model describing random surfaces, which arises as the 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 …