Ferenc Fodor: The volume of central diagonal sections of the n-cube

Abstract: We prove that the volume of central hyperplane sections of a
unit cube in R^n orthogonal to a diameter of the cube is a strictly
monotonically increasing function of the dimension for sufficiently
large n. Our argument uses the integral formula of Ball for the volume
of central sections of the cube, and Laplace's method to estimate the
asymptotic behaviour of Ball's integral. This is joint work with
Bernardo Gonzales Merino (Murcia, Spain).