Brownian absolute continuity of the KPZ fixed point with arbitrary initial condition
Sourav Sarkar, Bálint Virág
Abstract
We show that the law of the KPZ fixed point starting from arbitrary initial condition is absolutely continuous with respect to the law of Brownian motion B on every compact interval. In particular, the Airy1 process is absolutely continuous with respect to B on any compact interval.
Topics & Concepts
MathematicsAbsolute continuityBrownian motionInterval (graph theory)Mathematical analysisFractional Brownian motionDiffusion processModulus of continuityBrownian excursionGeometric Brownian motionCombinatoricsType (biology)StatisticsComputer scienceInnovation diffusionBiologyEcologyKnowledge managementRandom Matrices and ApplicationsStochastic processes and statistical mechanicsStochastic processes and financial applications