Geodesic
On the probabilistic representation of the resolvent of the two-dimensional Schr\"odinger operator
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 140-158

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We consider a family of random linear operators that arises in the construction of a probabilistic representation of the resolvent of the two-dimensional Schrödinger operator. It is shown that with probability one the operators of this family are integral operators in $L_2(\mathbb{R}^2)$. The properties of the kernels of the corresponding operators are also investigated. 
@article{ZNSL_2023_526_a8,
     author = {A. K. Nikolaev},
     title = {On the probabilistic representation of the resolvent of the two-dimensional {Schr\"odinger} operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {140--158},
     publisher = {mathdoc},
     volume = {526},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a8/}
}
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A. K. Nikolaev. On the probabilistic representation of the resolvent of the two-dimensional Schr\"odinger operator. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 140-158. http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a8/