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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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Point-to-line polymers and orthogonal Whittaker functions
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by Elia Bisi and Nikos Zygouras PDF
Trans. Amer. Math. Soc. 371 (2019), 8339-8379 Request permission

Abstract:

We study a one-dimensional directed polymer model in an inverse-gamma random environment, known as the log-gamma polymer, in three different geometries: point-to-line, point-to-half-line and when the polymer is restricted to a half-space with end point lying free on the corresponding half-line. Via the use of A. N. Kirillov’s geometric Robinson-Schensted-Knuth correspondence, we compute the Laplace transform of the partition functions in the above geometries in terms of orthogonal Whittaker functions, thus obtaining new connections between the ubiquitous class of Whittaker functions and exactly solvable probabilistic models. In the case of the first two geometries we also provide multiple contour integral formulae for the corresponding Laplace transforms. Passing to the zero-temperature limit, we obtain new formulae for the corresponding last passage percolation problems with exponential weights.
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Additional Information
  • Elia Bisi
  • Affiliation: Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom
  • MR Author ID: 1215838
  • Email: elia.bisi@ucd.ie
  • Nikos Zygouras
  • Affiliation: Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom
  • MR Author ID: 843972
  • Email: N.Zygouras@warwick.ac.uk
  • Received by editor(s): April 14, 2017
  • Received by editor(s) in revised form: July 31, 2017, and September 13, 2017
  • Published electronically: February 27, 2019
  • Additional Notes: The work of the first author was supported by EPSRC via grant EP/M506679/1.
    The work of the second author was supported by EPSRC via grant EP/L012154/1.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 8339-8379
  • MSC (2010): Primary 60Cxx, 05E05, 82B23; Secondary 11Fxx, 82D60
  • DOI: https://doi.org/10.1090/tran/7423
  • MathSciNet review: 3955549