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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Observables of Macdonald processes
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by Alexei Borodin, Ivan Corwin, Vadim Gorin and Shamil Shakirov PDF
Trans. Amer. Math. Soc. 368 (2016), 1517-1558 Request permission

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
  • MR Author ID: 604024
  • 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
  • MR Author ID: 833613
  • 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
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 1517-1558
  • MSC (2010): Primary 05E05
  • DOI: https://doi.org/10.1090/tran/6359
  • MathSciNet review: 3449217