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 20 of 28 for “"Scaling limit"”.
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Scaling limit of critical systems in random geometry
This thesis focusses on the properties of, and relationships between, several fundamental objects arising from critical physical models. In particular, we consider Schramm--Loewner evolutions, the Gaussian free field, Liouville quantum gravity and the Brownian continuum random tree. We begin by …
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Cardy embedding of random planar maps and a KPZ formula for mated trees
… 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 (RPM). First, we study …
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Integrability in random conformal geometry
… 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 field theory …
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Universal Scaling Limits of the Symplectic Elliptic Ginibre Ensemble
… the questions of how to compute the microscopic scaling limit and whether it is universal.
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Topics in Combinatorics and Random Matrix Theory
… theory are given. These include Regev's single scaling limit, Gessel's Toeplitz determinant identity, and Rains' integral representation. The double scaling limit (Baik-Deift-Johansson theorem) is briefly described, although we have no new results in that direction. Following up on the …
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Conformally invariant scaling limits of random curves and correlations
This thesis studies scaling limits of critical random models on planar graphs, when a fine-mesh graph approximates a planar domain. Such studies are motivated by quantum field theoretic predictions that suggest the emergence of intricate, conformally invariant structures from simple combinatorial …
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Fluctuations and mixing for planar random growth
… of random conformal maps. Following the scaling limit result of Norris and Turner (2012), who proved that the limiting shape of large HL(0) clusters is a disc, we show that the fluctuations around this deterministic shape are described by a random holomorphic Gaussian field $\mathcal{F}$ …
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Thick points of random walk and multiplicative chaos
… graphs. In higher dimensions, we study the scaling limit of the set of thick points. In particular, we show that the rescaled number of thick points converges to a nondegenerate random variable and that the centred maximum of the local times converges to a randomly shifted Gumbel …
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Homogenization of Random Media: Random Walks, Diffusions and Stochastic Interface Models
… concerns homogenization results, in particular scaling limits and heat kernel estimates, for random processes moving in random environments and for stochastic interface models. The first chapter will survey recent research and introduce three models of interest: the random conductance model, the …
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Stochastic Surface Growth
… scale invariance with universal exponents and limiting distributions. For a special, exactly solvable growth model (polynuclear growth - PNG) on a one-dimensional substrate (1+1 dimensional) we confirm the known scaling exponents and identify for the first time the limiting distributions of …
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New Classical Solutions in Supergravity
… manifolds. These reductions are from a scaling limit of the famous spherical reductions, and can be solely supported by warp factors. The second class contains a large number of String/M theory solutions that have Lifshitz or Schrodinger scaling symmetry, obtained from marginally …
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Quadratic differentials and Loewner evolutions
… Loewner evolution (SLE) in 1999 as the scaling limit of many important 2-dimensional random processes on lattices has opened up an exciting area of research. One of the central ideas in his theory is the use of a classic tool in function theory, the Loewner differential equation (LDE), …
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On the metric structure of random planar maps and SLE-decorated Liouville quantum gravity
… a critical percolation interface converge in the scaling limit to [square root of]8/3- LQG surfaces decorated by SLE8/3 and SLE6, respectively, with respect to a generalization of the Gromov-Hausdorff topology. We also introduce an approach for analyzing certain random planar maps belonging to the …
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Applications of conformal field theory and string theory in statistical systems
… the free fermions in planar Ising model and its scaling limit at criticality. On the one hand, we examine the relation between the transfer matrix formalism and discrete holomorphicity. We show that the fermion operators of the Ising model satisfy a complexification of the defining relations of …
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Matings of negatively correlated trees with applications to Schnyder woods and bipolar orientations
… 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. First, we identify the covariance of the Brownian motion in the Mating of Trees …
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Conformal loop ensembles and the Gaussian free field
… 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 establish a new convergence result for percolation, a well-studied discrete model. We …
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Continuum Methods and Tightness Results for Non-Simple SLE and CLE: Existence, Interactions, and Metric Approximations
… 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 curves are self-touching and CLE loops …
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Scaling limits of random plane partitions and six-vertex models
We present a collection of results about the scaling limits of several models from integrable probability. Our first result concerns the asymptotic behavior of the bottom slice of a Hall-Littlewood random plane partition. We show the latter concentrates around a limit shape and in two different …
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Characterization of Dopant Diffusion in Bulk and lower dimensional Silicon Structures
The semiconductor industry scaling has mainly been driven by Moore's law, which states that the number of transistors on a single chip should double every year and a half to two years. Beyond 2011, when the channel length of the Metal Oxide Field effect transistor (MOSFET) approaches 16 nm, the …
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AB initio study and design of 2D materials/III-nitrides-based post-CMOS devices using first-principles multiphysics simulation framework
As logic devices are nearing their physical scaling limit, many new materials and novel device-operation concepts have been proposed lately. Among the most promising candidates, two-dimensional (2D) materials-based tunnel FETs (TFETs) are especially in the spotlight nowadays. In this dissertation, …
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