Why random matrices share universal processes with interacting particle systems?

Abstract

In these lecture we explain why limiting distribution function, like the Tracy-Widom distribution, or limit processes, like the Airy_2 process, arise both in random matrices and interacting particle systems. The link is through a common mathematical structure on an interlacing structure, also known as Gelfand-Tsetlin pattern, that appears for specific models in both fields.

Extended lecture notes of the ICTP minicourse in Trieste, September 2013. 45 pages, 6 figures; Minor corrections

References in corpus (4)

• Fluctuation properties of the TASEP with periodic initial configuration
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Slow decorrelations in KPZ growth
• From interacting particle systems to random matrices

Cited by in corpus (5)

• Height fluctuations for the stationary KPZ equation
• A limit theorem at the spectral edge for corners of time-dependent Wigner matrices
• An introduction to random matrix theory
• From the totally asymmetric simple exclusion process to the KPZ fixed point
• Eigenvalue fluctuations for random regular graphs