Determinantal Structures in the O’Connell-Yor Directed Random Polymer Model

We study the semi-discrete directed random polymer model introduced by O’Connell and Yor. We obtain a representation for the moment generating function of the polymer partition function in terms of a determinantal measure. This measure is an extension of the probability measure of the eigenvalues fo...

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Bibliographic Details
Published in:Journal of statistical physics 2016-05, Vol.163 (4), p.675-713
Main Authors: Imamura, Takashi, Sasamoto, Tomohiro
Format: Article
Language:English
Subjects:
Analysis
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Polymer industry
Polymers
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:We study the semi-discrete directed random polymer model introduced by O’Connell and Yor. We obtain a representation for the moment generating function of the polymer partition function in terms of a determinantal measure. This measure is an extension of the probability measure of the eigenvalues for the Gaussian unitary ensemble in random matrix theory. To establish the relation, we introduce another determinantal measure on larger degrees of freedom and consider its few properties, from which the representation above follows immediately.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-016-1492-1