Log-Gamma Polymer Free Energy Fluctuations via a Fredholm Determinant Identity
Original manuscript June 20, 2012
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Springer-Verlag
2013
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| Online Access: | http://hdl.handle.net/1721.1/80868 https://orcid.org/0000-0002-2913-5238 |
| _version_ | 1826197791763857408 |
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| author | Borodin, Alexei Corwin, Ivan Remenik, Daniel |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Corwin, Ivan Remenik, Daniel |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | Original manuscript June 20, 2012 |
| first_indexed | 2024-09-23T10:53:12Z |
| format | Article |
| id | mit-1721.1/80868 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:53:12Z |
| publishDate | 2013 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/808682022-09-27T15:42:50Z Log-Gamma Polymer Free Energy Fluctuations via a Fredholm Determinant Identity Borodin, Alexei Corwin, Ivan Remenik, Daniel Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Corwin, Ivan Original manuscript June 20, 2012 We prove that under n[superscript 1/3] scaling, the limiting distribution as n → ∞ of the free energy of Seppalainen’s log-Gamma discrete directed polymer is GUE Tracy-Widom. The main technical innovation we provide is a general identity between a class of n-fold contour integrals and a class of Fredholm determinants. Applying this identity to the integral formula proved in Corwin et al. (Tropical combinatorics and Whittaker functions. http://arxiv.org/abs/1110.3489v3 [math.PR], 2012) for the Laplace transform of the log-Gamma polymer partition function, we arrive at a Fredholm determinant which lends itself to asymptotic analysis (and thus yields the free energy limit theorem). The Fredholm determinant was anticipated in Borodin and Corwin (Macdonald processes. http://arxiv.org/abs/1111.4408v3 [math.PR], 2012) via the formalism of Macdonald processes yet its rigorous proof was so far lacking because of the nontriviality of certain decay estimates required by that approach. National Science Foundation (U.S.) (Grant DMS-1056390) National Science Foundation (U.S.) (Grant DMS-1208998) Clay Mathematics Institute (Research Fellowship) Microsoft Research (Schramm Memorial Fellowship) 2013-09-23T16:21:46Z 2013-09-23T16:21:46Z 2013-07 2012-11 Article http://purl.org/eprint/type/JournalArticle 0010-3616 1432-0916 http://hdl.handle.net/1721.1/80868 Borodin, Alexei, Ivan Corwin, and Daniel Remenik. “Log-Gamma Polymer Free Energy Fluctuations via a Fredholm Determinant Identity.” Communications in Mathematical Physics (July 3, 2013). https://orcid.org/0000-0002-2913-5238 en_US http://dx.doi.org/10.1007/s00220-013-1750-x Communications in Mathematical Physics Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Borodin, Alexei Corwin, Ivan Remenik, Daniel Log-Gamma Polymer Free Energy Fluctuations via a Fredholm Determinant Identity |
| title | Log-Gamma Polymer Free Energy Fluctuations via a Fredholm Determinant Identity |
| title_full | Log-Gamma Polymer Free Energy Fluctuations via a Fredholm Determinant Identity |
| title_fullStr | Log-Gamma Polymer Free Energy Fluctuations via a Fredholm Determinant Identity |
| title_full_unstemmed | Log-Gamma Polymer Free Energy Fluctuations via a Fredholm Determinant Identity |
| title_short | Log-Gamma Polymer Free Energy Fluctuations via a Fredholm Determinant Identity |
| title_sort | log gamma polymer free energy fluctuations via a fredholm determinant identity |
| url | http://hdl.handle.net/1721.1/80868 https://orcid.org/0000-0002-2913-5238 |
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