Skip Navigation

International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn017, 67 pages, doi:10.1093/imrn/rnn017 published on March 10, 2008
This Article
Right arrow Full Text (PDF)
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Its, A. R.
Right arrow Articles by Östensson, J.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Critical Edge Behavior in Unitary Random Matrix Ensembles and the Thirty-Fourth Painlevé Transcendent

Alexander R. Its1, Arno B. J. Kuijlaars2 and Jörgen Östensson3

1 Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, Indianapolis, IN 46202-3216, USA
2 Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium
3 Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, Sweden

Correspondence: Correspondence to be sent to: arno.kuijlaars{at}wis.kuleuven.be

We describe a new universality class for unitary invariant random matrix ensembles. It arises in the double scaling limit of ensembles Formula , with {alpha} > – 1/2, defined on n x n Hermitian matrices M. Assuming that the limiting mean eigenvalue density is regular and that the origin is a right endpoint of its support, we compute the limiting eigenvalue correlation kernel in the double scaling limit as n, N -> {infty} such that n2/3(n/N – 1) = O(1). We use the Deift–Zhou steepest descent method for the Riemann–Hilbert problem for polynomials orthogonal with respect to the weight |x|2{alpha}e–NV(x). Our main attention is on the construction of a local parametrix near the origin by means of the {psi}-functions associated with a distinguished solution of the Painlevé XXXIV equation.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.