### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 012, 12 pages      arXiv:2110.07456      https://doi.org/10.3842/SIGMA.2022.012

### A Quantum $0-\infty$ Law

Michel Bauer ab
a) Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique, 91191 Gif-sur-Yvette, France
b) PSL Research University, CNRS, École normale supérieure, Département de mathématiques et applications, 75005 Paris, France

Received October 27, 2021, in final form February 01, 2022; Published online February 10, 2022

Abstract
We give conditions under which a sequence of randomly chosen orthogonal subspaces of a separable Hilbert space generates the whole space.

Key words: random Hamiltonians; random geometry; Markov processes.

pdf (384 kb)   tex (19 kb)

References

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2. Ross S., A first course in probability, 10th ed., Pearson, 2019.
3. Srednicki M., Chaos and quantum thermalization, Phys. Rev. E 50 (1994), 888-901, arXiv:cond-mat/9403051.