Mod-ϕ Convergence

1. Introduction
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

2. Preliminaries
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

3. Fluctuations in the case of lattice distributions
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

4. Fluctuations in the non-lattice case
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

5. An extended deviation result from bounds on cumulants
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

6. A precise version of the Ellis-Gärtner theorem
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

7. Examples with an explicit generating function
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

8. Mod-Gaussian convergence from a factorisation of the probability generating function
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

9. Dependency graphs and mod-Gaussian convergence
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

10. Subgraph count statistics in Erdős-Rényi random graphs
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

11. Random character values from central measures on partitions
Valentin Féray, Pierre-Loïc Méliot, Ashkan Nikeghbali

Keywords: Mathematics, Probability Theory and Stochastic Processes, Number Theory, Combinatorics, Linear and Multilinear Algebras, Matrix Theory