Electronic Communications in Probability

Ergodicity of the Airy line ensemble

Ivan Corwin and Xin Sun

Full-text: Open access

Abstract

In this paper, we establish the ergodicity of the Airy line ensemble with respect to horizontal shifts. This shows that it is the only candidate for Conjecture 3.2 in Corwin & Hammond, Invent. Math. 2014, regarding the classification of ergodic line ensembles satisfying a certain Brownian Gibbs property after a parabolic shift.

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 49, 11 pp.

Dates
Accepted: 26 July 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316751

Digital Object Identifier
doi:10.1214/ECP.v19-3504

Mathematical Reviews number (MathSciNet)
MR3246968

Zentralblatt MATH identifier
1303.82020

Subjects
Primary: 82C22: Interacting particle systems [See also 60K35]
Secondary: 82B23: Exactly solvable models; Bethe ansatz

Keywords
the Airy line ensemble ergodicity Gibbs measure extremal

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Corwin, Ivan; Sun, Xin. Ergodicity of the Airy line ensemble. Electron. Commun. Probab. 19 (2014), paper no. 49, 11 pp. doi:10.1214/ECP.v19-3504. https://projecteuclid.org/euclid.ecp/1465316751


Export citation

References

  • Borodin, Alexei. Determinantal point processes. The Oxford handbook of random matrix theory, 231–249, Oxford Univ. Press, Oxford, 2011.
  • Ivan Corwin and Alan Hammond. KPZ line ensemble. arXiv preprint arXiv:1312.2600, 2013.
  • Corwin, Ivan; Hammond, Alan. Brownian Gibbs property for Airy line ensembles. Invent. Math. 195 (2014), no. 2, 441–508.
  • Corwin, Ivan; Quastel, Jeremy; Remenik, Daniel. Continuum statistics of the ${\rm Airy}_ 2$ process. Comm. Math. Phys. 317 (2013), no. 2, 347–362.
  • Georgii, Hans-Otto. Gibbs measures and phase transitions. Second edition. de Gruyter Studies in Mathematics, 9. Walter de Gruyter & Co., Berlin, 2011. xiv+545 pp. ISBN: 978-3-11-025029-9
  • Halmos, Paul R. Measure Theory. D. Van Nostrand Company, Inc., New York, N. Y., 1950. xi+304 pp.
  • Johansson, Kurt. Discrete polynuclear growth and determinantal processes. Comm. Math. Phys. 242 (2003), no. 1-2, 277–329.
  • PrÄ‚Å›hofer, Michael; Spohn, Herbert. Scale invariance of the PNG droplet and the Airy process. Dedicated to David Ruelle and Yasha Sinai on the occasion of their 65th birthdays. J. Statist. Phys. 108 (2002), no. 5-6, 1071–1106.
  • Jermey Quastel and Daniel Remenik. Airy processes and variational problems. arXiv preprint arXiv:1301.0750, 2013.
  • Scheidemann, Volker. Introduction to complex analysis in several variables. Birkhäuser Verlag, Basel, 2005. viii+171 pp. ISBN: 978-3-7643-7490-7; 3-7643-7490-X