Disjoint optimizers and the directed landscape / Duncan Dauvergne, Lingfu Zhang.

Format:

Book

Author/Creator:

Dauvergne, Duncan, author.

Zhang, Lingfu, author.

Series:

Memoirs of the American Mathematical Society ; v. 1524.

Memoirs of the American Mathematical Society, 0065-9266 ; v. 1524

Language:

English

Subjects (All):

Mathematical optimization.

Geometry, Plane.

Physical Description:

v, 103 pages : illustrations ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2024

Summary:

We study maximal length collections of disjoint paths, or 'disjoint optimizers', in the directed landscape. We show that disjoint optimizers always exist, and that their lengths can be used to construct an extended directed landscape. The extended directed landscape can be built from an independent collection of extended Airy sheets, which we define from the parabolic Airy line ensemble. We show that the extended directed landscape and disjoint optimizers are scaling limits of the corresponding objects in Brownian last passage percolation (LPP). As two consequences of this work, we show that one direction of the Robinson-Schensted-Knuth bijection passes to the KPZ limit, and we find a criterion for geodesic disjointness in the directed landscape that uses only a single parabolic Airy line ensemble. The proofs rely on a new notion of multi-point LPP across the parabolic Airy line ensemble, combinatorial properties of multi-point LPP, and probabilistic resampling ideas.

Contents:

Chapter 1. Introduction

Chapter 2. Last passage percolation across lines

Chapter 3. Tightness

Chapter 4. Last passage percolation across the parabolic Airy line ensemble

Chapter 5. Limits of Melon optimizers and the Extended Airy Sheet

Chapter 6. The Scaling Limit of Multi-point Brownian LPP

Chapter 7. Paths in the Extended landscape

Chapter 8. Disjointness of optimizers

Chapter 9. Convergence of optimizers

Appendix A. Appendix

Bibliography.

Notes:

Includes bibliographical references.

ISBN:

1470471906

9781470471903

OCLC:

1477767517