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010 a| 2022023085;

020 a| 9781470452292q| (paperback);

020 z| 9781470470951q| (pdf);

035 a| (WaSeSS)ssj0002689214;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QA274.75b| .H366 2022;

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100 1 a| Hammond, Alan,d| 1976-?| UNAUTHORIZED;

245 10 a| Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolationh| [electronic resource] /c| Alan Hammond.;

260 a| Providence, RI :b| American Mathematical Society,c| [2022];

300 a| v, 133 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| number 1363;

500 a| "May 2022, volume 277, number 1363 (fourth of 6 numbers).";

504 a| Includes bibliographical references (page 131-133).;

505 0 a| Brownian Gibbs ensembles : definition and statements -- Missing closed middle reconstruction and the Wiener candidate -- The jump ensemble method : foundations -- The jump ensemble method : applications.;

506 a| Available only to authorized users.;

520 a| "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 Airy2 process, describes after the subtraction of a parabola the limiting law of the scaled energy of a geodesic running from the origin to a variable point on an anti-diagonal line in such problems as Poissonian last passage percolation. The ensemble of curves resulting from the Airy line ensemble after the subtraction of the same parabola enjoys a simple and explicit spatial Markov property, the Brownian Gibbs property. 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Brownian motion processes.=| ^A88606;

650 0 a| Gibbs' equation.=| ^A280118;

650 0 a| Airy functions.=| ^A602609;

650 0 a| Set theory.=| ^A26682;

650 0 a| Percolation (Statistical physics)=| ^A232246;

650 0 a| Geodesics (Mathematics)=| ^A283230;

650 0 a| Stochastic partial differential equations.=| ^A269969;

650 7 a| Statistical mechanics, structure of matter -- Time-dependent statistical mechanics (dynamic and nonequilibrium) -- Interacting particle systems.2| msc;

650 7 a| Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Exactly solvable models; Bethe ansatz.2| msc;

650 7 a| Probability theory and stochastic processes -- Stochastic analysis -- Stochastic partial differential equations.2| msc;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=29731907;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6511863-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/14/2025x| EBOOKz| JERESOURCE;

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

Author/creator	Hammond, Alan, 1976-
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, [2022]
Description	v, 133 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Brownian motion processes. Gibbs' equation. Airy functions. Set theory. Percolation (Statistical physics) Geodesics (Mathematics) Stochastic partial differential equations.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; number 1363
Contents	Brownian Gibbs ensembles : definition and statements -- Missing closed middle reconstruction and the Wiener candidate -- The jump ensemble method : foundations -- The jump ensemble method : applications.
Abstract	"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 Airy2 process, describes after the subtraction of a parabola the limiting law of the scaled energy of a geodesic running from the origin to a variable point on an anti-diagonal line in such problems as Poissonian last passage percolation. The ensemble of curves resulting from the Airy line ensemble after the subtraction of the same parabola enjoys a simple and explicit spatial Markov property, the Brownian Gibbs property. 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"-- Provided by publisher.
General note	"May 2022, volume 277, number 1363 (fourth of 6 numbers)."
Bibliography note	Includes bibliographical references (page 131-133).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022023085
ISBN	9781470452292 (paperback)
ISBN	(pdf)

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

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