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Observables of Macdonald processes


Authors: Alexei Borodin, Ivan Corwin, Vadim Gorin and Shamil Shakirov
Journal: Trans. Amer. Math. Soc. 368 (2016), 1517-1558
MSC (2010): Primary 05E05
Published electronically: June 18, 2015
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Abstract: We present a framework for computing averages of various observables of Macdonald processes. This leads to new contour-integral formulas for averages of a large class of multilevel observables, as well as Fredholm determinants for averages of two different single level observables.


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Additional Information

Alexei Borodin
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 – and – Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow, Russia
Email: borodin@math.mit.edu

Ivan Corwin
Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027 – and – Clay Mathematics Institute, 10 Memorial Boulevard, Suite 902, Providence, Rhode Island 02903 – and – Institut Henri Poincaré, 11 Rue Pierre et Marie Curie, 75005 Paris, France
Email: ivan.corwin@gmail.com

Vadim Gorin
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 – and – Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow, Russia
Email: vadicgor@gmail.com

Shamil Shakirov
Affiliation: Department of Mathematics, University of California Berkeley, Berkeley, California 94720
Email: shakirov@itep.ru

DOI: https://doi.org/10.1090/tran/6359
Received by editor(s): June 10, 2013
Received by editor(s) in revised form: December 6, 2013, and December 16, 2013
Published electronically: June 18, 2015
Dedicated: To the memory of A. Zelevinsky
Article copyright: © Copyright 2015 American Mathematical Society