Brownian Regularity for the Airy Line Ensemble, and Multi-Polymer Watermelons in Brownian Last Passage Percolation.

Cover
Title page
Chapter 1. Introduction
1.1. Kardar-Parisi-Zhang universality
1.2. A conceptual overview of the scaled Brownian last passage percolation study
1.3. Non-intersecting line ensembles and their integrable and probabilistic analysis
1.4. The article's main results
Chapter 2. Brownian Gibbs ensembles: Definition and statements
2.1. Preliminaries: Bridge ensembles and the Brownian Gibbs property
2.2. Statements of principal results concerning regular ensembles
2.3. Some generalities: Notation and basic properties of Brownian Gibbs ensembles
Chapter 3. Missing closed middle reconstruction and the Wiener candidate
3.1. Close encounter between finitely many non-intersecting Brownian bridges
3.2. The reconstruction of the missing closed middle
3.3. Applications of the Wiener candidate approach
Chapter 4. The jump ensemble method: Foundations
4.1. The jump ensemble method
4.2. General tools for the jump ensemble method
Chapter 5. The jump ensemble method: Applications
5.1. Upper bound on the probability of curve closeness over a given point
5.2. Closeness of curves at a general location
5.3. Brownian bridge regularity of regular ensembles
Appendix A. Properties of regular Brownian Gibbs ensembles
A.1. Scaled Brownian LPP line ensembles are regular
A.2. The lower tail of the lower curves
A.3. Regular ensemble curves collapse near infinity
Bibliography
Back Cover.