### Abstract

Chapter 2 prepares the ground for the analysis of interacting particle systems carried out in Part II. The authors introduce here the principal technical tools of the single-particle multi-scale analysis (MSA), developed over the last thirty years by the mathematical community. The analytical tools of the so-called variable-energy MSA, developed in late 1980s, are streamlined and complemented by a simpler, fixed-energy approach. A simple and comprehensive derivation of the spectral and strong dynamical localization from the fixed-energy MSA, suitable for adaptations to interacting systems, is presented for the first time in mathematical literature.

Original language | English (US) |
---|---|

Title of host publication | Progress in Mathematical Physics |

Publisher | Birkhauser Boston |

Pages | 27-133 |

Number of pages | 107 |

DOIs | |

Publication status | Published - Jan 1 2014 |

### Publication series

Name | Progress in Mathematical Physics |
---|---|

Volume | 65 |

ISSN (Print) | 1544-9998 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics

### Cite this

*Progress in Mathematical Physics*(pp. 27-133). (Progress in Mathematical Physics; Vol. 65). Birkhauser Boston. https://doi.org/10.1007/978-1-4614-8226-0_2