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Universal distribution of random matrix eigenvalues near the 'birth of a cut' transition

B Eynard

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We study the eigenvalue distribution of a random matrix, at a transition where a new connected component of the eigenvalue density support appears away from other connected components. Unlike previously studied critical points, which correspond to rational singularities ρ(x) ~ xp/q classified by conformal minimal models and integrable hierarchies, this transition shows logarithmic and non-analytical behaviours. There is no critical exponent; instead, the power of N changes in a sawtooth behaviour.


 
A commentary on this article has been published by R Flume and A Klitz, 2008 J. Stat. Mech. N10001.
Keywords

conformal field theory

matrix models

 

E-print Number: math-ph/0605064

Cited: by |

Refers: to

PACS

02.10.Yn Matrix theory

02.10.Ud Linear algebra

05.70.Jk Critical point phenomena

MSC

37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

15A52 Random matrices

82B27 Critical phenomena

15A18 Eigenvalues, singular values, and eigenvectors

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 07 (July 2006)

Received 1 June 2006, accepted for publication 27 June 2006

Published 17 July 2006



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