Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 
 

 

Point-to-line polymers and orthogonal Whittaker functions


Authors: Elia Bisi and Nikos Zygouras
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
Published electronically: February 27, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 60Cxx, 05E05, 82B23, 11Fxx, 82D60

Retrieve articles in all journals with MSC (2010): 60Cxx, 05E05, 82B23, 11Fxx, 82D60


Additional Information

Elia Bisi
Affiliation: Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: elia.bisi@ucd.ie

Nikos Zygouras
Affiliation: Department of Statistics, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: N.Zygouras@warwick.ac.uk

DOI: https://doi.org/10.1090/tran/7423
Keywords: Point-to-line log-gamma polymers, orthogonal Whittaker functions, geometric Robinson-Schensted-Knuth correspondence, Bump-Stade identity, Ishii-Stade identity
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.
Article copyright: © Copyright 2019 American Mathematical Society