Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random orthonormal bases of spaces of high dimension   We consider a sequence H_N of Hilbert spaces of dimensions d_N tending to
infinity. The motivating examples are eigenspaces or quasi-mode spaces of a
Laplace or Schrodinger operator. We define a random ONB of H_N by fixing one
ONB and changing it by a random element of U(d_N). A random ONB of the direct
sum of the H_N is an independent sequence {U_N} of random ONB's of the H_N. We
prove that if d_N tends to infinity and if the normalized traces of observables
in H_N tend to a unique limit state, then a random ONB also tends to that limit
state. This generalizes an earlier result of the author for eigenspaces of the
standard 2-sphere, and shows that the result does not depend on how fast the
dimensions grow. In particular it is valid for eigenspaces of a flat rational
torus in dimensions > 4. The main idea is to convert quantum ergodicity into a
problem on the moments of inertia of permutahedra and to calculate the moments
using Schur polynomials.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: cs