The parabolic Anderson model on Riemann surfaces

2017/02/09 by Dahlqvist, Antoine, Diehl, Joscha, Driver, Bruce · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1702.02965

Abstract

We show well-posedness for the parabolic Anderson model on 2-dimensional closed Riemannian manifolds. To this end we extend the notion of regularity structures to curved space, and explicitly construct the minimal structure required for this equation. A central ingredient is the appropriate re-interpretation of the polynomial model, which we build up to any order.

Cited by

• Renormalisation of singular SPDEs with Correlated Coefficients
• On the Spectral Geometry and Small Time Mass of Anderson Models on Planar Domains
• Parabolic Anderson Model in the Hyperbolic Space. Part II: Quenched Asymptotics

Related

• Global Geometry within an SPDE Well-Posedness Problem
• Global well-posedness for the nonlinear generalized parabolic Anderson model equation
• Quasilinear generalized parabolic Anderson model equation
• Global well-posedness for 2D generalized Parabolic Anderson Model via paracontrolled calculus
• Parabolic Anderson model in bounded domains of recurrent metric measure spaces