Archive ouverte UNIGE | last documentshttps://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGEengSelf-similar corrections to the ergodic theorem for the Pascal-Adic transformationhttps://archive-ouverte.unige.ch/unige:6383https://archive-ouverte.unige.ch/unige:6383Let T be the Pascal-adic transformation. For any measurable function g, we consider the corrections to the ergodic theorem sum_{k=0}^{j-1} g(T^k x) - j/l sum_{k=0}^{l-1} g(T^k x). When seen as graphs of functions defined on {0,...,l-1}, we show for a suitable class of functions g that these quantities, once properly renormalized, converge to (part of) the graph of a self-affine function. The latter only depends on the ergodic component of x, and is a deformation of the so-called Blancmange function. We also briefly describe the links with a series of works on Conway recursive $10,000 sequence.Tue, 27 Apr 2010 12:33:43 +0200