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 8 of 8 for “"Random geometry"”.
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Random geometry in two and three dimensions
A central theme in random geometry is the interplay between discrete models and continuum ones that appear in scaling limits. Surprising structure and symmetry often arises in these scaling limits, leading to an interplay between combinatorics, probability, complex analysis, and geometry. The dimer …
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Exploring Random Geometry with the Gaussian Free Field
This thesis studies the geometry of objects from 2-dimensional statistical physics in 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 …
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Scaling limit of critical systems in random geometry
… 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 system displays a phase transition in the branching rate: …
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Frontiers of Liouville quantum gravity
Abstract This thesis studies a universal model 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 …
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Conformal welding of random surfaces from Liouville theory
… 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 scaling …
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Disorder in holographic field theories: inhomogeneous geometries, momentum relaxation and SYK models
… breaking translational symmetry in the dual geometry. In particular, we focus on an example in which the dual geometry is similar to anti-de Sitter (AdS) Brans-Dicke theory. We study the thermodynamic and transport properties of the model and show that for strong momentum relaxation and low …
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Macroscopic behaviour of Lipschitz random surfaces
A random field is a random function φ from the square lattice ℤᵈ to some fixed standard Borel space (E, ℰ). A random surface is a random field with the extra condition that E ∈ {ℤ, ℝ} where ℰ is the standard σ-algebra. For random surfaces, one often studies the gradient ∇φ of the random function of …
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Continuum Methods and Tightness Results for Non-Simple SLE and CLE: Existence, Interactions, and Metric Approximations
… 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 of SLEκ curves and CLEκ loops in the non-simple regime κ∈(4,8], where the …