标题： Holley--Stroock 唯一性方法对于$\varphi^4_2$动力学的应用 显示英文标题

标题： Holley--Stroock uniqueness method for the $\varphi^4_2$ dynamics

摘要： Holley-Stroock 倡导的方法通过一致的对数Sobolev不等式确立了格点自旋系统Glauber动力学不变测度的唯一性。 我们利用这种方法证明了在临界温度以下（由有限易感性刻画）$\varphi^4_2$SPDE 不变测度的唯一性。 该方法需要三个要素：一致的对数Sobolev不等式（已知）、传播速度估计以及时间$1$下有限体积动力学律相对于有限体积不变测度的相对熵粗略估计。 后两个要素在格点上被广泛理解，但证明无法推广到SPDE，这里针对$\varphi^4_2$动力学进行了建立。 显示英文摘要

摘要： The approach initiated by Holley--Stroock establishes the uniqueness of invariant measures of Glauber dynamics of lattice spin systems from a uniform log-Sobolev inequality. We use this approach to prove uniqueness of the invariant measure of the $\varphi^4_2$ SPDE up to the critical temperature (characterised by finite susceptibility). The approach requires three ingredients: a uniform log-Sobolev inequality (which is already known), a propagation speed estimate, and a crude estimate on the relative entropy of the law of the finite volume dynamics at time $1$ with respect to the finite volume invariant measure. The last two ingredients are understood very generally on the lattice, but the proofs do not extend to SPDEs, and are here established in the instance of the $\varphi^4_2$ dynamics.