Arinkin, D. and Borodin, A. (2009) τ-function of discrete isomonodromy transformations and probability. Compositio Mathematica, 145 (3). pp. 747-772. ISSN 0010-437X http://resolver.caltech.edu/CaltechAUTHORS:20090730-112214062
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Abstract
We introduce the τ-function of a difference rational connection (d-connection) and its isomonodromy transformations. We show that in a continuous limit ourτ-function agrees with the Jimbo–Miwa–Ueno τ-function. We compute the τ-function for the isomonodromy transformations leading to difference Painlevé V and difference Painlevé VI equations. We prove that the gap probability for a wide class of discrete random matrix type models can be viewed as the τ-function for an associated d-connection.
| Item Type: | Article |
|---|---|
| Additional Information: | © 2009 Foundation Compositio Mathematica. Received 13 March 2008, accepted in nal form 16 July 2008, published online 19 February 2009. The authors are very grateful to Pierre Deligne for illuminating discussions. We are particularly indebted to him for interpreting the τ-function via determinant of cohomology. |
| Subject Keywords: | discrete Painlevé equations; τ-functions |
| Record Number: | CaltechAUTHORS:20090730-112214062 |
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20090730-112214062 |
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| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 14741 |
| Collection: | CaltechAUTHORS |
| Deposited By: | Jason Perez |
| Deposited On: | 07 Aug 2009 17:43 |
| Last Modified: | 26 Dec 2012 11:07 |
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