The Φ34 measure via Girsanov’s theorem
Nikolay Barashkov, Massimiliano Gubinelli
Abstract
We construct the Φ34 measure on a periodic three dimensional box as an absolutely continuous perturbation of a random translation of the Gaussian free field. The shifted measure is constructed via Girsanov’s theorem and the relevant filtration is the one generated by a scale parameter. As a byproduct we give a self-contained proof that the Φ34 measure is singular wrt. the Gaussian free field.
Topics & Concepts
Girsanov theoremMathematicsGaussian free fieldMeasure (data warehouse)Gaussian measureAbsolute continuityGaussianPerturbation (astronomy)Mathematical analysisPure mathematicsStochastic differential equationData miningPhysicsQuantum mechanicsComputer scienceadvanced mathematical theoriesMathematical Dynamics and FractalsStochastic processes and financial applications