Access the full text.
Sign up today, get DeepDyve free for 14 days.
Ivan Corwin, A. Hammond (2011)
Brownian Gibbs property for Airy line ensemblesInventiones mathematicae, 195
J. Baik, Zhipeng Liu (2017)
Multipoint distribution of periodic TASEPJournal of the American Mathematical Society
P. Ferrari, A. Occelli (2017)
Universality of the GOE Tracy-Widom distribution for TASEP with arbitrary particle densityarXiv: Probability
Riddhipratim Basu, C. Hoffman, A. Sly (2018)
Nonexistence of Bigeodesics in Integrable Models of Last Passage Percolation
P. Ferrari, H. Spohn (2016)
On Time Correlations for KPZ Growth in One DimensionSymmetry Integrability and Geometry-methods and Applications, 12
K. Johansson (1999)
Transversal fluctuations for increasing subsequences on the planeProbability Theory and Related Fields, 116
P. Dey, Mathew Joseph, R. Peled (2018)
Longest increasing path within the critical striparXiv: Probability
P. Ferrari, A. Occelli (2018)
Time-time Covariance for Last Passage Percolation with Generic Initial ProfileMathematical Physics, Analysis and Geometry, 22
A. Hammond (2016)
Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolationMemoirs of the American Mathematical Society
Leandro Pimentel (2017)
Local Behavior of Airy ProcessesarXiv: Probability
K. Johansson (2015)
Two Time Distribution in Brownian Directed PercolationCommunications in Mathematical Physics, 351
M. Ledoux, B. Rider (2009)
Small deviations for beta ensemblesElectronic Journal of Probability, 15
K. Matetski, J. Quastel, Daniel Remenik (2016)
The KPZ fixed pointActa Mathematica
K. Johansson (2019)
Long and Short Time Asymptotics of the Two-Time Distribution in Local Random GrowthMathematical Physics, Analysis and Geometry, 23
S. Chatterjee, P. Dey (2009)
Central limit theorem for first-passage percolation time across thin cylindersProbability Theory and Related Fields, 156
Correlation of the airy 2 process in time
Riddhipratim Basu, V. Sidoravicius, A. Sly (2014)
Last Passage Percolation with a Defect Line and the Solution of the Slow Bond ProblemarXiv: Probability
E. Cator, Leandro Pimentel (2013)
On the local fluctuations of last-passage percolation modelsStochastic Processes and their Applications, 125
The following statement is true uniformly in all large C, k, and r
K. Johansson (1999)
Shape Fluctuations and Random MatricesCommunications in Mathematical Physics, 209
J Baik (2014)
91
Riddhipratim Basu, S. Ganguly, A. Hammond (2017)
The Competition of Roughness and Curvature in Area-Constrained Polymer ModelsCommunications in Mathematical Physics, 364
the above set up, for j ≥ 1, and 1 ≤ ≤ 2 j , we have P
J. Baik, P. Ferrari, S. Péché (2012)
Convergence of the Two-Point Function of the Stationary TASEParXiv: Mathematical Physics
A. Borodin, Patrik Caltech, Wias Berlin (2007)
Large time asymptotics of growth models on space-like paths I: PushASEPElectronic Journal of Probability, 13
Leandro Pimentel (2018)
Local Behaviour of Airy ProcessesJournal of Statistical Physics, 173
K. Johansson (2018)
The two-time distribution in geometric last-passage percolationProbability Theory and Related Fields
[For directed last passage percolation on ℤ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb {Z}^2$$ \end{document} with exponential passage times on the vertices, let Tn denote the last passage time from (0, 0) to (n, n). We consider asymptotic two point correlation functions of the sequence Tn. In particular we consider Corr(Tn, Tr) for r ≤ n where r, n →∞ with r ≪ n or n − r ≪ n. Establishing a conjecture from Ferrari and Spohn (SIGMA 12:074, 2016), we show that in the former case Corr(Tn,Tr)=Θ((rn)1∕3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathrm {Corr}(T_{n}, T_{r})=\varTheta ((\frac {r}{n})^{1/3})$$ \end{document} whereas in the latter case 1−Corr(Tn,Tr)=Θ((n−rn)2∕3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$1-{\mathrm {Corr}}(T_{n}, T_{r})=\varTheta ((\frac {n-r}{n})^{2/3})$$ \end{document}. The argument revolves around finer understanding of polymer geometry and is expected to go through for a larger class of integrable models of last passage percolation. As a by-product of the proof, we also get quantitative estimates for locally Brownian nature of pre-limits of Airy2 process coming from exponential LPP, a result of independent interest.]
Published: Nov 4, 2020
Keywords: Last passage percolation; Time correlation; KPZ universality class
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.