Project Maroon

Welcome to the wiki page of

Project Maroon
Approximation results in probability theory and quantum physics

coordinated by Markus Haase (Delft).

The group members are:

  • Björn Augner (Karlsruhe)
  • Christoph Schuhmacher (Chemniz)
  • Stefan Manuel Tomaszewski (Tübingen)

The project description can be downloaded from here.

Discussion of Project Maroon.

 

The Trotter–Kato approximation theorems and the Chernoff product formula can be used to give proofs for some results in probability theory (Central Limit Theorem, Weak Law of Large Numbers) and in quantum physics (Feynman Path Formula). These ideas go back to works of Trotter [6] (in the first case) and Nelson [5] (in the second) and were developed in papers of Goldstein [3, 2, 4], inspired by [1].

The aim of this project is to give a concise presentation of these results building on Goldstein’s papers and the ISEM notes as background material.

References

  1. P. L. Butzer, W. Dickmeis, L. Hahn, and R. J. Nessel. Lax-type theorems and a unified approach to some limit theorems in probability theory with rates. ResultateMath., 2(1):30–53, 1979.
  2. Jerome A. Goldstein. Corrigendum on: “Semigroup-theoretic proofs of the central limit theorem and other theorems of analysis” (Semigroup Forum 12 (1976), no. 3, 189-206). Semigroup Forum, 12(4):388, 1976.
  3. Jerome A. Goldstein. Semigroup-theoretic proofs of the central limit theorem and other theorems of analysis. Semigroup Forum, 12(3):189–206, 1976.
  4. Jerome A. Goldstein. A semigroup-theoretic proof of the law of large numbers. Semigroup Forum, 15(1):89–90, 1977/78.
  5. Edward Nelson. Feynman integrals and the Schr ̈dinger equation. J. Mathematical Phys., 5:332–343, 1964.
  6. H. F. Trotter. An elementary proof of the central limit theorem. Arch. Math., 10:226–234, 1959.
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