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The Gauss-Kuzmin statistics for the triangle map (a type of multidimensionalcontinued fraction algorithm) are derived by examining the leadingeigenfunction of the triangle map's transfer operator. The technical difficultyis finding the appropriate Banach space of functions. We also show that, bythinking of the triangle map's transfer operator as acting on a one-dimensionalfamily of Hilbert spaces, the transfer can be thought of as a family of nuclearoperators of trace class zero.

On Gauss-Kuzmin Statistics and the Transfer Operator for a Multidimensional Continued Fraction Algorithm: the Triangle Map