Gradient-type estimates for the dynamic φ⁴₂-model

2022/02/22 by Kunick, Florian, Tsatsoulis, Pavlos
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2202.11036

Abstract

We prove gradient bounds for the Markov semigroup of the dynamic φ⁴₂-model on a torus of fixed size L>0. For sufficiently large mass m>0 these estimates imply exponential contraction of the Markov semigroup. Our method is based on pathwise estimates of the linearized equation. To compensate the lack of exponential integrability of the stochastic drivers we use a stopping time argument and the strong Markov property in the spirit of Cass--Litterer--Lyons. Following the classical approach of Bakry-Émery, as a corollary we prove a Poincaré/spectral gap inequality for the φ⁴₂-measure of sufficiently large mass m>0 with almost optimal carré du champ.

Related

• The Markov property for φ⁴₃ on the cylinder
• Gradient estimates for SDEs without monotonicity type conditions
• Ergodicity of the Anderson Φ₂⁴ model
• Dirichlet form associated with the Φ₃⁴ model
• Entrance measures for semigroups of time-inhomogeneous SDEs: possibly degenerate and expanding