Here we have some notes in the reading of the paper Macdonald Processes by Borodin and Corwin.

Note 1, the definition of Macdonald processes and Macdonald measure.

Note 2, the definition and properties of q-Whittaker processes.

Note 3, the evolution of Macdonald processes by the multivariate Markov process, and the relation to TASEP and q-TASEP.

Note 4, The Whittaker processes as limits of q-Whittaker processes.

Note 5, The relation to semi-discrete directed polymer and the Tracy-Widom universality. This is the last note, and is even more hasty than others.


Last modified: Mon 18 May 14:44:51 Singapore time 2020 by WANG Dong