English

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.

Keywords

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

R2 v1 2026-06-21T18:43:18.547Z