Geodesic
Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 78-81.

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Two approaches are suggested for constructing a probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$, in the strong operator topology. In the first approach, the approximating operators have the form of expectations of functionals of a certain Poisson point field, while, in the second approach, the approximating operators have the form of expectations of functionals of sums of independent identically distributed random variables with finite moments of order $2m+2$.
Keywords: Schrödinger equation, Poisson random measures, limit theorems. 
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     title = {Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
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M. V. Platonova; S. V. Tsykin. Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 78-81. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a15/

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