Discrete Malliavin–Stein method: Berry–Esseen bounds for random graphs and percolation
| Autor: | Christoph Thäle, Anselm Reichenbachs, Kai Krokowski |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Rademacher functional 82B43 05C80 central limit theorem 01 natural sciences 010104 statistics & probability percolation 60H07 Mathematics::Probability 60F05 Mehler’s formula 0101 mathematics Mathematics Central limit theorem Random graph Discrete mathematics Degree (graph theory) Semigroup 010102 general mathematics Malliavin–Stein method Tree (graph theory) tree Nonlinear system sub-graph count Percolation Berry–Esseen bound Statistics Probability and Uncertainty random graph |
| Zdroj: | Ann. Probab. 45, no. 2 (2017), 1071-1109 |
| Popis: | A new Berry–Esseen bound for nonlinear functionals of nonsymmetric and nonhomogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin–Stein method and an analysis of the discrete Ornstein–Uhlenbeck semigroup. The result is applied to sub-graph counts and to the number of vertices having a prescribed degree in the Erdős–Renyi random graph. A further application deals with a percolation problem on trees. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|