Airy kernel with two sets of parameters in directed percolation and random matrix theory

Abstract

We introduce a generalization of the extended Airy kernel with two sets of real parameters. We show that this kernel arises in the edge scaling limit of correlation kernels of determinantal processes related to a directed percolation model and to an ensemble of random matrices.

figures improved; references and comments added

References in corpus (10)

• Shape Fluctuations and Random Matrices
• Discrete polynuclear growth and determinantal processes
• Level-Spacing Distributions and the Airy Kernel
• Eynard-Mehta theorem, Schur process, and their pfaffian analogs
• Random matrices and determinantal processes
• Matrices coupled in a chain. I. Eigenvalue correlations
• Differential Equations for Dyson Processes
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• Universal Parametric correlations at the soft edge of the spectrum of random matrix ensembles
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Cited by in corpus (46)

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• Two speed TASEP
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• Time-time covariance for last passage percolation with generic initial profile
• Convergence of the two-point function of the stationary TASEP
• General beta Jacobi corners process and the Gaussian Free Field
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• Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization
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• Multiplicative functionals on ensembles of non-intersecting paths
• Fluctuations of the log-gamma polymer free energy with general parameters and slopes
• On the largest-eigenvalue process for generalized Wishart random matrices
• Determinantal Correlations for Classical Projection Processes
• On the principal components of sample covariance matrices
• Directed last passage percolation with discontinuous weights
• Shock fluctuations in flat TASEP under critical scaling
• Convergence of the Environment Seen from Geodesics in Exponential Last-Passage Percolation
• Temporal Correlation in Last Passage Percolation with Flat Initial Condition via Brownian Comparison
• Darboux transformations and random point processes
• Brownian Gibbs property for Airy line ensembles
• Interlaced particle systems and tilings of the Aztec diamond
• Generalized Green Functions and current correlations in the TASEP
• Limit shapes for inhomogeneous corner growth models with exponential and geometric weights
• Perturbed GUE Minor Process and Warren's Process with Drifts
• Stochastic growth in time dependent environments
• Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
• Moderate deviation and exit time estimates for stationary Last Passage Percolation
• Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures
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• Singular values for products of two coupled random matrices: hard edge phase transition
• On the exponent governing the correlation decay of the Airy${}_1$ process
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• Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles
• Correlation kernels for sums and products of random matrices
• Volume of the set of LOCC-convertible quantum states
• Limit distributions for KPZ growth models with spatially homogeneous random initial conditions
• Borodin-Péché fluctuations of the free energy in directed random polymer models
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• Limit shape and fluctuations for exactly solvable inhomogeneous corner growth models
• Batch latency analysis and phase transitions for a tandem of queues with exponentially distributed service times