Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolation

The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are given by the multi-line Airy process. It is a natural object in the KPZ universality class: for example, its highest curve, the Airy In this paper, we employ the Brownia...

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Bibliographic Details
Main Author: Hammond, Alan
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2022
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Airy functions
Brownian motion processes
Geodesics (Mathematics)
Gibbs' equation
Percolation (Statistical physics)
Probability theory and stochastic processes > Stochastic analysis > Stochastic partial differential equations. msc
Set theory
Statistical mechanics, structure of matter > Equilibrium statistical mechanics > Exactly solvable models; Bethe ansatz. msc
Statistical mechanics, structure of matter > Time-dependent statistical mechanics (dynamic and nonequilibrium) > Interacting particle systems. msc
Stochastic partial differential equations
multi-line Airy process
Brownian last passage percolation
Airy line ensemble
polymer weight and geometry
eigenvalue deviation bounds
ISBN:9781470452292, 1470452294
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Table of Contents:
  • Introduction -- Brownian Gibbs ensembles: Definition and statements -- Missing closed middle reconstruction and the Wiener candidate -- The jump ensemble method: Foundations -- The jump ensemble method: Applications -- Properties of regular Brownian Gibbs ensembles
  • 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