2008/09/22 by Gregory F. Lawler 路 1 citation
Mathematics 路 Physics and Astronomy 路 #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Markov Chains and Monte Carlo Methods #Invariant (physics) #Criticality #Scaling #Scale invariance #Conformal map #Conformal symmetry #Statistical physics #Mathematics #Conformal field theory #Theoretical physics #Physics #Scaling dimension #Mathematical physics #Mathematical analysis #Quantum mechanics #Geometry #Nuclear physics
paper 路 pdf 路 doi:10.1090/s0273-0979-08-01229-9
openalex publication_date 2008/09/22 路 openalex created_date 2025/10/10 路 openalex updated_date 2026/07/07
A number of two-dimensional models in statistical physics are conjectured to have scaling limits at criticality that are in some sense conformally invariant. In the last ten years, the rigorous understanding of such limits has increased significantly. I give an introduction to the models and one of the major new mathematical structures, the Schramm-Loewner Evolution ( <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S upper L upper E"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>L</mml:mi> <mml:mi>E</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">SLE</mml:annotation> </mml:semantics> </mml:math> </inline-formula> ).