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Abstract
We study unitary invariant random matrix ensembles with singular potentials. We obtain asymptotics for the partition functions associated to the Laguerre and Gaus sian Unitary Ensembles perturbed with a pole of order k at the origin, in the double scaling limit where the size of the matrices grows, and at the same time the strength of the pole decreases at an appropriate speed. In addition, we obtain double scaling asymptotics of the correlation kernel for a general class of ensembles of positivedefinite Hermitian matrices perturbed with a pole. Our results are described in terms of a hier archy of higher order analogs to the PIII equation, which reduces to the PIII equation itself when the pole is simple.
Original language  English 

Pages (fromto)  23202375 
Number of pages  56 
Journal  International Mathematics Research Notices 
Volume  2016 
Issue number  8 
Early online date  14 Jul 2015 
DOIs  
Publication status  Published  Aug 2016 
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Dive into the research topics of 'Random matrix ensembles with singularities and a hierarchy of Painlevé III equations'. Together they form a unique fingerprint.Projects
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Professor Francesco Mezzadri
 Probability, Analysis and Dynamics
 School of Mathematics  Professor of Mathematical Physics
 Applied Mathematics
 Mathematical Physics
Person: Academic , Member