Conditional gaugeability and subcriticality of generalized Schrödinger operators
There exists a wealth of connections between the quantum mechanics (or rather theory of Schrödinger and Schrödinger-type operators) and statistical physics (in particular, stochastic processes etc). The paper is devoted to this class of problems. One should not feel discouraged by an unfortunate presentation of the results: It makes sense to glimpse in some related references first (and, in particular, in the last one). Then, still, one should probably skip the incomprehensible introduction and read the paper in a non-sequential, ``direct-access'' manner. In my case I enjoyed the reading started by the introductory part of the last Section 4 (large deviation principle for symmetric Markov processes) which set me in the game. Before waiting till the end of section (Onegin was famous for that) I was then able to see the point: The paper is about the existence of Greens functions (disguised under the name of ``subcriticality''). Moving more deeply and technically in the text one may then pick up any of its subjects: the review of the concept of gaugeability (Section 2) and the study of its conditional version (in Section 3). The reward: One sees necessary and sufficient conditions for things named in the title and, finally, indulges oneself in the subtleties of the key illustrative example 3.10.
necessary and sufficient conditions of subcriticality
scientific article; zbMATH DE number 1797593
scientific article