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

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.

preprint2013arXivOpen access
Grigori Olshanski
math.RTmath-phmath.PRmath.MP
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Grigori Olshanski

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