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arXiv · 1612.03114

Brownian Motion and Finite Approximations of Quantum Systems over Local Fields

Erik M. Bakken·Trond Digernes·David Weisbart
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Abstract

We give a stochastic proof of the finite approximability of a class of Schr\"odinger 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.

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Erik M. Bakken, Trond Digernes, David Weisbart. 2016-12-09. Brownian Motion and Finite Approximations of Quantum Systems over Local Fields. https://doi.org/10.1142/s0129055x17500167

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