Maximum and coupling of the sine-Gordon field
Roland Bauerschmidt, Michael Hofstetter
Abstract
For 0<β<6π, we prove that the distribution of the centred maximum of the ε-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel distribution as ε→0. Our proof relies on a strong coupling at all scales of the sine-Gordon field with the Gaussian free field, of independent interest, and extensions of existing methods for the maximum of the lattice Gaussian free field.
Topics & Concepts
Gaussian free fieldMathematicsGumbel distributionTorusSineGaussianMathematical physicsField (mathematics)MaximaCoupling (piping)Lattice (music)Distribution (mathematics)Mathematical analysisPure mathematicsExtreme value theoryQuantum mechanicsStatisticsGeometryPhysicsEngineeringPerformance artAcousticsArt historyArtMechanical engineeringGeometry and complex manifoldsGeometric Analysis and Curvature FlowsStochastic processes and statistical mechanics