Published May 2009
| Version Submitted
Journal Article
Open
τ-function of discrete isomonodromy transformations and probability
Creators
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1.
University of North Carolina at Chapel Hill
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2.
California Institute of Technology
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.
Additional Information
© 2009 Foundation Compositio Mathematica. Received 13 March 2008, accepted in final 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.Attached Files
Submitted - 0706.3073.pdf
Files
0706.3073.pdf
Additional details
Additional titles
- Alternative title
- Tau-function of discrete isomonodromy transformations and probability
Identifiers
- Eprint ID
- 14741
- Resolver ID
- CaltechAUTHORS:20090730-112214062
Related works
- Describes
- https://arxiv.org/abs/0706.3073 (URL)
Dates
- Created
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2009-08-07Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field