Local Gaussian fluctuations in the Airy and discrete PNG processes

DOI10.1214/07-AOP353zbMath1142.60025arXivmath/0701880MaRDI QIDQ2427058

Jonas Hägg

Publication date: 15 May 2008

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701880

zbMATH Keywords

stationary processPNG process

Mathematics Subject Classification ID

Gaussian processes (60G15) Stationary stochastic processes (60G10) Random matrices (algebraic aspects) (15B52)

Related Items (20)

Airy Processes and Variational Problems ⋮ Ergodicity of the KPZ Fixed Point ⋮ Local behavior and hitting probabilities of the \(\text{Airy}_1\) process ⋮ Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolation ⋮ Modulus of continuity of polymer weight profiles in Brownian last passage percolation ⋮ Stochastic analysis of infinite particle systems—A new development in classical stochastic analysis and dynamical universality of random matrices ⋮ Local and global comparisons of the Airy difference profile to Brownian local time ⋮ Brownian Gibbs property for Airy line ensembles ⋮ Long and short time asymptotics of the two-time distribution in local random growth ⋮ Tail of the two-time height distribution for KPZ growth in one dimension ⋮ Local behaviour of Airy processes ⋮ Asymptotics for the covariance of the Airy\(_{2}\) process ⋮ On the numerical evaluation of Fredholm determinants ⋮ Tracy-Widom distribution, Airy\(_2\) process and its sample path properties ⋮ On the local fluctuations of last-passage percolation models ⋮ Brownian absolute continuity of the KPZ fixed point with arbitrary initial condition ⋮ On time correlations for KPZ growth in one dimension ⋮ A PATCHWORK QUILT SEWN FROM BROWNIAN FABRIC: REGULARITY OF POLYMER WEIGHT PROFILES IN BROWNIAN LAST PASSAGE PERCOLATION ⋮ Fluctuations of the competition interface in presence of shocks ⋮ Stochastic geometry and dynamics of infinitely many particle systems—random matrices and interacting Brownian motions in infinite dimensions

Cites Work

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• Discrete polynuclear growth and determinantal processes
• Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges
• Shape fluctuations and random matrices
• The arctic circle boundary and the Airy process
• PDEs for the joint distributions of the Dyson, Airy and Sine processes
• Determinantal random point fields
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix

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