Edge statistics for a class of repulsive particle systems

DOI10.1007/s00440-017-0765-1zbMath1456.60022arXiv1501.07501OpenAlexW2963937786MaRDI QIDQ2413240

Martin Venker, Thomas Kriecherbauer

Publication date: 10 April 2018

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

Full work available at URL: https://arxiv.org/abs/1501.07501

zbMATH Keywords

random matricesuniversalitylarge deviationsmoderate deviationsAiry kernelTracy-Widom distribution

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Interacting particle systems in time-dependent statistical mechanics (82C22)

Related Items (6)

An update on local universality limits for correlation functions generated by unitary ensembles ⋮ Precise deviations results for the maxima of some determinantal point processes: the upper tail ⋮ Critical behavior of non-intersecting Brownian motions ⋮ Boundary asymptotics of non-intersecting Brownian motions: Pearcey, Airy and a transition ⋮ Universality in several-matrix models via approximate transport maps ⋮ Convergence and asymptotic approximations to universal distributions in probability

Cites Work

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• Precise deviations results for the maxima of some determinantal point processes: the upper tail
• Edge universality of beta ensembles
• Local universality of repulsive particle systems and random matrices
• First-order global asymptotics for confined particles with singular pair repulsion
• Universality in several-matrix models via approximate transport maps
• Small deviations for beta ensembles
• Orthogonal and symplectic matrix models: universality and other properties
• Particle systems with repulsion exponent \(\beta\) and random matrices
• A note on the second order universality at the edge of Coulomb gases on the plane
• Empirical spacings of unfolded eigenvalues
• Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
• Level-spacing distributions and the Airy kernel
• On the statistical mechanics approach in the random matrix theory: Integrated density of states.
• Correlation functions, cluster functions, and spacing distributions for random matrices
• Asymptotics for Christoffel functions with varying weights
• Optimal tail estimates for directed last passage site percolation with geometric random variables
• Moderate deviations for longest increasing subsequences: The lower tail
• Shape fluctuations and random matrices
• On fluctuations of eigenvalues of random Hermitian matrices.
• Abstract loop equations, topological recursion and new applications
• Transport maps for \(\beta\)-matrix models and universality
• On analytic characteristic functions
• Global Asymptotics for the Christoffel-Darboux Kernel of Random Matrix Theory
• Beta ensembles, stochastic Airy spectrum, and a diffusion
• Large-NAsymptotic Expansion for Mean Field Models with Coulomb Gas Interaction
• Universality of the Stochastic Airy Operator
• An Introduction to Random Matrices
• Moderate deviations for longest increasing subsequences: The upper tail
• Random matrices: The Universality phenomenon for Wigner ensembles
• Random Fields and Geometry
• Random matrices, log-gases and Holder regularity
• AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION

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