The Airy_1 process is not the limit of the largest eigenvalue in GOE matrix diffusion

Abstract

Using a systematic approach to evaluate Fredholm determinants numerically, we provide convincing evidence that the Airy_1-process, arising as a limit law in stochastic surface growth, is not the limit law for the evolution of the largest eigenvalue in GOE matrix diffusion.

14 pages, 3 figures

References in corpus (7)

• On the Numerical Evaluation of Fredholm Determinants
• Fluctuation properties of the TASEP with periodic initial configuration
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
• A determinantal formula for the GOE Tracy-Widom distribution
• PDEs for the joint distributions of the Dyson, Airy and Sine processes
• The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process

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• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• On the Numerical Evaluation of Distributions in Random Matrix Theory: A Review
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• From interacting particle systems to random matrices
• Experimental approaches to universal out-of-equilibrium scaling laws: turbulent liquid crystal and other developments
• Universal fluctuations in KPZ growth on one-dimensional flat substrates
• On Time Correlations for KPZ Growth in One Dimension
• A Pfaffian representation for flat ASEP
• Reflected Brownian motions in the KPZ universality class
• Kardar-Parisi-Zhang Interfaces with Inward Growth
• Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz
• Accessing Kardar-Parisi-Zhang universality sub-classes with exciton polaritons
• The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises
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• A limit theorem at the spectral edge for corners of time-dependent Wigner matrices
• Shock fluctuations in flat TASEP under critical scaling
• On the partial connection between random matrices and interacting particle systems
• KPZ universality class and the anchored Toom interface
• Why random matrices share universal processes with interacting particle systems?
• Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
• Radial Restricted Solid-on-Solid and Etching Interface Growth Models
• On the exponent governing the correlation decay of the Airy${}_1$ process
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