Lectures on integrable probability

By Alexei Borodin, Vadim Gorin. 2012

166 citations recorded by the source corpus.

These are lecture notes for a mini-course given at the St. Petersburg School in Probability and Statistical Physics in June 2012. Topics include integrable models of random growth, determinantal point processes, Schur processes and Markov dynamics on them, Macdonald processes and their application to asymptotics of directed polymers in random media.

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Citations in the corpus

Height Fluctuations for the Stationary KPZ Equation (2014, methodology): “and proved the 1/3 ﬂuctuation exponent for a wide class of KPZ initial data. A brief review and comparison of methods 1, 2 and 4 can be found in [34], whereas some aspects of method 3 are reviewed in [26,28]. See also the review [35]. Besides the narrow-wedge initial data, there are a few other type”
Stochastic six-vertex model (2014, methodology): “systems including Asymmetric Simple Exclusion Process (ASEP) [TW4], [BCS], q{TASEP [BC], [FV], and the solution to KPZ stochastic partial dierential equation [ACQ], [SS], [D], [CDR], [BCF]; see also [BG2], [BP], [Cor3] for reviews. The process Xb 1;b 2(t) has a limit to ASEP when b 1 !0 with b 2=b 1”
Representations of classical Lie groups and quantized free convolution (2013, background): “section are based on the remarkable connection between the Gelfand{Tsetlin bases in irreducible representations and the enumeration of lozenge tilings of planar domains, cf. [CLP, Section 2] and also [BG2], [BP]. Consider a strip of width N drawn on the regular triangular lattice, whose left boundar”