Let
be an irrational of ``diophantine type'', for example
.
For N large, consider the N numbers in [0,1),
,
.
Order these as
.
Do the normalized consecutive spacings
behave like spacings between random numbers? So for example, does the distribution of the consecutive spacings tend to the density ? This problem arises in connection with the spacing distribution for the eigenvalues of quantizations of completely integrable Hamiltonians, and was raised by physicists.
ROBERT LIPSHITZ'S INVESTIGATIONS