Markov dynamics on the dual object to the infinite-dimensional unitary group

Abstract

These are notes for a mini-course of 3 lectures given at the St. Petersburg School in Probability and Statistical Physics (June 2012). My aim was to explain, on the example of a particular model, how ideas from the representation theory of big groups can be applied in probabilistic problems. The material is based on the joint paper arXiv:1009.2029 by Alexei Borodin and myself; a broader range of topics is surveyed in the lecture notes by Alexei Borodin and Vadim Gorin arXiv:1212.3351.

24 pp

References in corpus (4)

• Zeros of Airy Function and Relaxation Process
• Markov property of determinantal processes with extended sine, Airy, and Bessel kernels
• Markov processes of infinitely many nonintersecting random walks
• Moment problems and boundaries of number triangles

Cited by in corpus (1)

• The Gelfand-Tsetlin graph and Markov processes