Random conformal weldings

DOI10.1007/s11511-012-0069-3zbMath1253.30032arXiv0909.1003OpenAlexW2043939288WikidataQ101067937 ScholiaQ101067937MaRDI QIDQ416846

Kari Astala, Antti Kupiainen, Eero Saksman, Peter W. Jones

Publication date: 10 May 2012

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.1003

zbMATH Keywords

quasiconformal mapsSLEconformal welding

Mathematics Subject Classification ID

Quasiconformal mappings in the complex plane (30C62) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

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Cites Work

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• Conformal weldings of random surfaces: SLE and the quantum gravity zipper
• Conformal invariance in random cluster models. I: Holomorphic fermions in the Ising model
• Brownian measures on Jordan-Virasoro curves associated to the Weil-Petersson metric
• Liouville quantum gravity and KPZ
• The boundary correspondence under quasiconformal mappings
• Probability tails of Gaussian extrema
• Positive martingales and random measures
• Sur certaines martingales de Benoit Mandelbrot
• Sharper bounds for Gaussian and empirical processes
• Log-infinitely divisible multifractal processes
• Removability theorems for Sobolev functions and quasiconformal maps
• Scaling limits of loop-erased random walks and uniform spanning trees
• Canonical Brownian motion on the space of univalent functions and resolution of Beltrami equations by a continuity method along stochastic flows
• Scaling exponents and multifractal dimensions for independent random cascades
• On the boundary correspondence of quasiconformal mappings of domains bounded by quasicircles
• Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential
• Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier
• Hardy spaces, $A_\infty$, and singular integrals on chord-arc domains
• Welding of polygons and the type of Riemann surfaces

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