Brownian motion and finite approximations of quantum systems over local fields
Journal article, Peer reviewed
Accepted version
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Date
2017Metadata
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- Institutt for matematiske fag [2527]
- Publikasjoner fra CRIStin - NTNU [38679]
Original version
10.1142/S0129055X17500167Abstract
We give a stochastic proof of the finite approximability of a class of Schrödinger operators over a local field, thereby completing a program of establishing in a non-Archimedean setting corresponding results and methods from the Archimedean (real) setting. A key ingredient of our proof is to show that Brownian motion over a local field can be obtained as a limit of random walks over finite grids. Also, we prove a Feynman–Kac formula for the finite systems, and show that the propagator at the finite level converges to the propagator at the infinite level.