Local behavior and hitting probabilities of the \(\text{Airy}_1\) process

DOI10.1007/s00440-012-0466-8zbMath1285.60095arXiv1201.4709OpenAlexW1662384341MaRDI QIDQ389272

Daniel Remenik, Jeremy Quastel

Publication date: 20 January 2014

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.4709

zbMATH Keywords

Brownian motionFredholm determinant\(\text{Airy}_1\) process

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Sample path properties (60G17)

Related Items (19)

Airy Processes and Variational Problems ⋮ Renormalization fixed point of the KPZ universality class ⋮ Modulus of continuity of polymer weight profiles in Brownian last passage percolation ⋮ Continuum statistics of the Airy\(_{2}\) process ⋮ Integrable fluctuations in the KPZ universality class ⋮ Local and global comparisons of the Airy difference profile to Brownian local time ⋮ Supremum of the \(\mathrm{Airy}_{2}\) process minus a parabola on a half line ⋮ Non-intersecting Brownian bridges and the Laguerre orthogonal ensemble ⋮ TASEP fluctuations with soft-shock initial data ⋮ How flat is flat in random interface growth? ⋮ Local behaviour of Airy processes ⋮ Tails of the endpoint distribution of directed polymers ⋮ Multiplicative functionals on ensembles of non-intersecting paths ⋮ 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 ⋮ Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy-Widom GOE distribution ⋮ Fluctuations of the competition interface in presence of shocks ⋮ Height fluctuations for the stationary KPZ equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solving the KPZ equation
• Local Brownian property of the narrow wedge solution of the KPZ equation
• Fluctuations of the one-dimensional polynuclear growth model in half-space
• Two speed TASEP
• Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
• The \(\text{Airy}_{1}\) process is not the limit of the largest eigenvalue in GOE matrix diffusion
• Level-spacing distributions and the Airy kernel
• Scale invariance of the PNG droplet and the Airy process
• Discrete polynuclear growth and determinantal processes
• Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges
• On orthogonal and symplectic matrix ensembles
• Continuum statistics of the Airy\(_{2}\) process
• Endpoint distribution of directed polymers in \(1 + 1\) dimensions
• Supremum of the \(\mathrm{Airy}_{2}\) process minus a parabola on a half line
• Multiplicative functionals on ensembles of non-intersecting paths
• Local Gaussian fluctuations in the Airy and discrete PNG processes
• Brownian Gibbs property for Airy line ensembles
• Fluctuation properties of the TASEP with periodic initial configuration
• The one-dimensional KPZ equation and the Airy process
• Dynamic Scaling of Growing Interfaces
• Transition between Airy₁and Airy₂processes and TASEP fluctuations
• Limit process of stationary TASEP near the characteristic line
• Fluctuations in the Discrete TASEP with Periodic Initial Configurations and the Airy1 Process
• Limit processes for TASEP with shocks and rarefaction fans

This page was built for publication: Local behavior and hitting probabilities of the \(\text{Airy}_1\) process