From interacting particle systems to random matrices

DOI10.1088/1742-5468/2010/10/P10016zbMath1456.82657arXiv1008.4853MaRDI QIDQ3301132

Patrik Lino Ferrari

Publication date: 11 August 2020

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.4853

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random matrices (algebraic aspects) (15B52)

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Cites Work

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• On the partial connection between random matrices and interacting particle systems
• Two speed TASEP
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Scaling limit for the space-time covariance of the stationary totally asymmetric simple exclusion process
• The \(\text{Airy}_{1}\) process is not the limit of the largest eigenvalue in GOE matrix diffusion
• Large time asymptotics of growth models on space-like paths. I: Push ASEP
• Shock fluctuations in asymmetric simple exclusion
• Coupling the simple exclusion process
• An exactly solved model of three-dimensional surface growth in the anisotropic KPZ regime
• Level-spacing distributions and the Airy kernel
• Stochastic Burgers and KPZ equations from particle systems
• Scale invariance of the PNG droplet and the Airy process
• Discrete polynuclear growth and determinantal processes
• Limiting distributions for a polynuclear growth model with external sources
• On orthogonal and symplectic matrix ensembles
• Shape fluctuations and random matrices
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• Fluctuation properties of the TASEP with periodic initial configuration
• The arctic circle boundary and the Airy process
• Exact solution of the totally asymmetric simple exclusion process: shock profiles
• Large time asymptotics of growth models on space-like paths. II: PNG and parallel TASEP
• A pedestrian's view on interacting particle systems, KPZ universality and random matrices
• Dynamic Scaling of Growing Interfaces
• Transition between Airy₁and Airy₂processes and TASEP fluctuations
• Course 1 Random matrices and determinantal processes
• Limit process of stationary TASEP near the characteristic line
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• Current fluctuations for the totally asymmetric simple exclusion process
• Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure
• Slow decorrelations in Kardar–Parisi–Zhang growth