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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Summary: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 Brownian Gibbs property to make a close comparison between the Airy line ensemble’s curves after affine shift and Brownian bridge, proving the finiteness of a superpolynomially growing moment bound on Radon-Nikodym derivatives. We also determine the value of a natural exponent describing in Brownian last passage percolation the decay in probability for the existence of several near geodesics that are disjoint except for their common endpoints, where the notion of ‘near’ refers to a small deficit in scaled geodesic energy, with the parameter specifying this nearness tending to zero. To prove both results, we introduce a technique that may be useful elsewhere for finding upper bounds on probabilities of events concerning random systems of curves enjoying the Brownian Gibbs property. Several results in this article play a fundamental role in a further study of Brownian last passage percolation in three companion papers (Hammond 2017a,b,c), in which geodesic coalescence and geodesic energy profiles are investigated in scaled coordinates.
Bibliography:May 2022, volume 277, number 1363 (fourth of 6 numbers)
Includes bibliographical references (p. 131-133)
ISBN:9781470452292
1470452294
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1363