Information geometry and its applications

Pescara - 1-5 July 2002


Abstract

July 2 - 17.10-17.40
A. De Sanctis - Exact asymptotics on Zoll surfaces

One of the procedures used to derive asymptotic expansions of the characteristic function is the method of stationary phase (Barndorff-Nielsen and Cox, '89). Using the Morse Theory, this method requires that we locate the critical points of the original function and then we approximate the characteristic function by certain sums depending on the values of the function and its higher derivatives at critical points.

The problem of finding random variables for which the method of stationary phase produces the exact value of the characteristic function involves topological properties of the statistical manifold. For this the spheres of even dimension are privileged with respect to those of odd dimension (Donald St. P. Richards,'95).

We prove that the classical exactness result on two-dimensional sphere holds also for particular perturbations of the metric, and then of the random variable, the so-called "Zoll metrics". [an error occurred while processing this directive]