Toeplitz determinants, random growth and determinantal processes

Abstract

We summarize some of the recent developments which link certain problems in combinatorial theory related to random growth to random matrix theory.

References in corpus (4)

• Level-Spacing Distributions and the Airy Kernel
• Fredholm Determinants, Differential Equations and Matrix Models
• The shape of a typical boxed plane partition
• Statistical Self-Similarity of One-Dimensional Growth Processes

Cited by in corpus (12)

• The Pearcey Process
• Distribution functions for largest eigenvalues and their applications
• Differential Equations for Dyson Processes
• First passage percolation and competition models
• Increasing and Decreasing Subsequences of Permutations and Their Variants
• The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel
• Matrix Kernels for the Gaussian Orthogonal and Symplectic Ensembles
• From Gumbel to Tracy-Widom
• Shannon and Rényi entropy rates of stationary vector valued Gaussian random processes
• On Painleve Related Functions Arising in Random Matrix Theory
• Finite n Largest Eigenvalue Probability Distribution Function of Gaussian Ensembles
• On some special directed last-passage percolation models