Mod-$\phi$ convergence
Probability
2011-08-01 v2 Number Theory
Abstract
Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many applications, we discuss random matrix theory, some probabilistic models in number theory, the winding number of complex brownian motion and the classical situation of the central limit theorem, and a conjecture concerning the distribution of values of the Riemann zeta function on the critical line.
Cite
@article{arxiv.1107.5657,
title = {Mod-$\phi$ convergence},
author = {Freddy Delbaen and Emmanuel Kowalski and Ashkan Nikeghbali},
journal= {arXiv preprint arXiv:1107.5657},
year = {2011}
}
Comments
31 pages; updated a reference, add math.NT category