Essays about: "Schramm-Loewner Evolution"

Found 3 essays containing the words Schramm-Loewner Evolution.

1. 1. Random curves and their scaling limits

   University essay from KTH/Skolan för teknikvetenskap (SCI)

   Author : Jonatan Wächter; [2023]
   Keywords : Stochastic processes; Schramm-Loewner-Evolution; Random Walk; Brownian Motion; Harmonic Explorer;

   Abstract : We focus on planar Random Walks and some related stochastic processes. The discrete models are introduced and some of their core properties examined. We then turn to the question of continuous analogues, starting with the well-known convergence of the Random Walk to Brownian Motion. READ MORE

3. 2. Bieberbach's Theorem, Normal Families and Approximation by Single-Slit Maps

   University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

   Author : Robin Runyeon Odeberg; [2022]
   Keywords : complex analysis; Bieberbach s theorem; Bieberbach inequality; de Branges theorem; single-slit maps; univalent functions; normal families; Mathematics and Statistics;

   Abstract : The main purpose of this thesis is to prove the Bieberbach inequality using Grönwall’s area theorem, and discuss some consequences of the Montel’s theorem and Carathéodroty convergence theorem regarding single-slit maps, which is essential to the proof of de Branges’ theorem.... READ MORE

4. 3. Reduced Loewner Energies

   University essay from KTH/Matematik (Avd.)

   Author : Ellen Krusell; [2021]
   Keywords : Loewner Energy; Schramm-Loewner Evolution;

   Abstract : In 1999 Schramm introduced the one-parameter family of random planar chords known as Schramm-Loewner evolution (SLE(kappa)). More recently,Wang defined a functional on (deterministic) planar chords and loops called Loewner energy. The Loewner energy is the rate function of a large deviation principle on SLE(kappa) as kappa tends to 0. READ MORE