论文标题
动态$φ^4_2 $ -MODEL的梯度型估计值
Gradient-type estimates for the dynamic $φ^4_2$-model
论文作者
论文摘要
我们证明了动态$φ^4_2 $ -MODEL的Markov Semigroup的梯度界限，固定尺寸$ L> 0 $。对于足够大的质量$ m> 0 $，这些估计值意味着马尔可夫半群的指数收缩。我们的方法基于线性方程的路径估计。为了弥补随机驱动程序的缺乏指数的一致性，我们使用了停止的时间论点和强大的马尔可夫财产，以卡斯（Cass）的精神 - litterer-loneons。遵循Bakry-émery的经典方法，作为推论，我们证明了$φ^4_2 $的庞加莱/光谱差距不平等 - 与几乎最佳的CarréDuChamp的足够大的质量$ M> 0 $。
We prove gradient bounds for the Markov semigroup of the dynamic $φ^4_2$-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 $φ^4_2$-measure of sufficiently large mass $m>0$ with almost optimal carré du champ.
