We prove a priori estimates and, as sequel, existence of Euclidean Gibbs states for quantum lattice systems. For this purpose we develop a new analytical approach, the main tools of which are: first, a characterization of the Gibbs states in terms of their Radon-Nikodym derivatives under shift transformations as well as in terms of their logarithmic derivatives through integration by parts formulae, and second, the choice of appropriate Lyapunov functionals describing stabilization effects in the system. The latter technique becomes applicable since on the basis of the integration by parts formulae the Gibbs states are characterized as solutions of an infinite system of partial differential equations. Our existence result generalize essentially all previous ones. In particular, superquadratic growth of the interaction potentials is allowed and $N$-particle interactions for $N\in \mathbb{N}\cup \{\infty \}$ are included. We also develop abstract frames both for the necessary single spin space analysis and for the lattice analysis apart from their applications to our concrete models. Both types of general results obtained in these two frames should be also of their own interest in infinite dimensional analysis.
A priori positivity of solutions to a non-conservative stochastic thin-film equation
随机守恒律在证明非负解的存在性时往往具有挑战性。在J.Fischer和G. Grün（2018，随机薄膜方程正解的存在性，SIAM J. Math. Anal.），在二次迁移率情形下，建立了一类保守随机薄膜方程正鞅解的存在性。在这项工作中，我们专注于一个更大的类的迁移率（包括线性）的薄膜模型。为了做到这一点，我们需要引入非线性源势，从而获得薄膜方程的非保守版本。对于这个模型，我们假设存在一个充分正则的局部解（即，定义到一个停时$τ$），通过对源电位和噪声提供适当的条件，我们证明了这样的解可以推广到任何$T>0$，并且它是正的概率为1.提供了与上述参考工作的全面比较。
