Open Access
Issue |
ESAIM: PS
Volume 28, 2024
|
|
---|---|---|
Page(s) | 258 - 273 | |
DOI | https://doi.org/10.1051/ps/2024007 | |
Published online | 23 September 2024 |
- C.A. Tracy and H. Widom, Level-spacing distributions and the Airy kernel. Commun. Math. Phys. 159 (1994) 151–174. [CrossRef] [Google Scholar]
- K. Matetski, J. Quastel and D. Remenik, The KPZ fixed point. Acta Math. 227 (2021) 115–203. [CrossRef] [MathSciNet] [Google Scholar]
- K. Johansson, Discrete polynuclear growth and determinantal processes. Commun. Math. Phys. 242 (2003) 277–329. [CrossRef] [Google Scholar]
- C.A. Tracy and H. Widom, On orthogonal and symplectic matrix ensembles. Commun. Math. Phys. 177 (1996) 727–754. [CrossRef] [Google Scholar]
- G.B. Nguyen and D. Remenik, Non-intersecting Brownian bridges and the Laguerre orthogonal ensemble. Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 2005–2029. [CrossRef] [MathSciNet] [Google Scholar]
- W. FitzGerald and J. Warren, Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions. Probab. Theory Related Fields 178 (2020) 121–171. [CrossRef] [MathSciNet] [Google Scholar]
- J. Quastel and D. Remenik, Airy Processes and Variational Problems. Vol. 69 of Springer Proc. Math. Stat.. Springer, New York (2014) 121–171. [Google Scholar]
- G.B. Nguyen and D. Remenik, Extreme statistics of non-intersecting Brownian paths. Electron. J. Probab. 22 (2017) Paper No. 102, 40. [CrossRef] [Google Scholar]
- M. Adler, J. Delépine and P. van Moerbeke, Dyson’s nonintersecting Brownian motions with a few outliers. Commun. Pure Appl. Math. 62 (2009) 334–395. [CrossRef] [Google Scholar]
- M. Adler, P.L. Ferrari and P. van Moerbeke, Airy processes with wanderers and new universality classes. Ann. Probab. 38 (2010) 714–769. [CrossRef] [MathSciNet] [Google Scholar]
- P.J. Forrester, S.N. Majumdar and G. Schehr, Non-intersecting Brownian walkers and Yang–Mills theory on the sphere. Nuclear Phys. B 844 (2011) 500–526. [CrossRef] [MathSciNet] [Google Scholar]
- K. Liechty, Nonintersecting Brownian motions on the half-line and discrete Gaussian orthogonal polynomials. J. Stat. Phys. 147 (2012) 582–622. [CrossRef] [MathSciNet] [Google Scholar]
- K. Liechty, G.B. Nguyen and D. Remenik, Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy-Widom GOE distribution. Ann. Inst. Henri Poincaré Probab. Stat. 58 (2022) 2250–2283. [CrossRef] [MathSciNet] [Google Scholar]
- K. Liechty and D. Wang, Nonintersecting Brownian bridges between reflecting or absorbing walls. Adv. Math. 309 (2017) 155–208. [CrossRef] [MathSciNet] [Google Scholar]
- G. Schehr, S.N. Majumdar, A. Comtet and J. Randon-Furling, Exact distribution of the maximal height of p vicious walkers. Phys. Rev. Lett. 101 (2008) 150601, 4. [CrossRef] [Google Scholar]
- C.A. Tracy and H. Widom, Differential equations for Dyson processes. Commun. Math. Phys. 252 (2004) 7–41. [CrossRef] [Google Scholar]
- C.A. Tracy and H. Widom, Nonintersecting Brownian excursions. Ann. Appl. Probab. 17 (2007) 953–979. [CrossRef] [MathSciNet] [Google Scholar]
- J. Warren, Dyson’s Brownian motions, intertwining and interlacing. Electron. J. Probab. 12 (2007) 573–590. [CrossRef] [MathSciNet] [Google Scholar]
- A. Borodin, P.L. Ferrari and T. Sasamoto, Transition between Airy1 and Airy2 processes and TASEP fluctuations. Commun. Pure Appl. Math. 61 (2008) 1603–1629. [CrossRef] [Google Scholar]
- I. Corwin and A. Hammond, Brownian Gibbs property for Airy line ensembles. Invent. Math. 195 (2014) 441–508. [CrossRef] [MathSciNet] [Google Scholar]
- J. Quastel and D. Remenik, Supremum of the airy 2 process minus a parabola on a half line. J. Statist. Phys. 150 (2013) 442–456. [CrossRef] [Google Scholar]
- P.J. Forrester, Log-gases and Random Matrices. Vol. 34 of London Mathematical Society Monographs Series. Princeton University Press, Princeton, NJ (2010). [Google Scholar]
- I.M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 (2001) 295–327. [CrossRef] [MathSciNet] [Google Scholar]
- K. Johansson, Shape fluctuations and random matrices. Commun. Math. Phys. 209 (2000) 437–476. [CrossRef] [Google Scholar]
- A. Edelman and M. La Croix, The singular values of the GUE (less is more). Random Matrices Theory Appl. 4 (2015) 1550021, 37. [CrossRef] [Google Scholar]
- M.L. Mehta, Random Matrices. Vol. 142 of Pure and Applied Mathematics (Amsterdam), 3rd edn. Elsevier/Academic Press, Amsterdam (2004). [Google Scholar]
- P. Sosoe and U. Smilansky, On the spectrum of random anti-symmetric and tournament matrices. Random Matrices Theory Appl. 5 (2016) 1650010, 33. [CrossRef] [Google Scholar]
- I. Corwin, J. Quastel and D. Remenik, Continuum statistics of the Airy2 process. Commun. Math. Phys. 317 (2013) 347–362. [CrossRef] [Google Scholar]
- A. Borodin, P.L. Ferrari, M. Prähofer, T. Sasamoto and J. Warren, Maximum of Dyson Brownian motion and non-colliding systems with a boundary. Electron. Commun. Probab. 14 (2009) 486–494. [CrossRef] [MathSciNet] [Google Scholar]
- NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/. Online companion to [37]. [Google Scholar]
- B. Simon, Trace Ideals and their Applications. Vol. 120 of Mathematical Surveys and Monographs, 2nd edn. American Mathematical Society (2005). [Google Scholar]
- A. Borodin, I. Corwin and D. Remenik, Multiplicative functionals on ensembles of non-intersecting paths. Ann. Inst. Henri Poincaré Probab. Stat. 51 (2015) 28–58. [CrossRef] [MathSciNet] [Google Scholar]
- K. Johansson, Random matrices and determinantal processes, in Mathematical Statistical Physics. Elsevier B.V., Amsterdam (2006) 1–55. [Google Scholar]
- Z.-y. Huang and J.-a. Yan, Introduction to Infinite Dimensional Stochastic Analysis. Vol. 502 of Mathematics and its Applications, Chinese edn. Kluwer Academic Publishers, Dordrecht; Science Press Beijing, Beijing (2000). [Google Scholar]
- G.E. Andrews, R. Askey and R. Roy, Special Functions. Vol. 71 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (1999). [Google Scholar]
- S. Roman, The Umbral Calculus. Vol. 111 of Pure and Applied Mathematics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York (1984). [Google Scholar]
- F.W.J. Olver, D.W. Lozier, R.F. Boisvert and C.W. Clark, editors, NIST handbook of mathematical functions. U.S. Department of Commerce, National Institute of Standards and Technology, Washington, DC; Cambridge University Press, Cambridge (2010). With 1 CD-ROM (Windows, Macintosh and UNIX). [Google Scholar]
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