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SUMMARY:Monodromies of ramified random coverings and geometry on partition
 s - Franck Gabriel (Warwick)
DTSTART:20151201T163000Z
DTEND:20151201T173000Z
UID:TALK62648@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Random monodromies of natural models of random ramified coveri
 ngs on the disk define a S(N)- valued planar Markovian holonomy fields. Ge
 neralizing a result of T. Levy about the asymptotic\, as N goes to infinit
 y\, of the Yang-Mills measure which is a special U(N)-valued planar Markov
 ian holonomy field\, we prove that the random monodromies of the considere
 d random ramified coverings converge in non-commutative distribution. In o
 rder to do so\, we will present a proof of the convergence of the eigenval
 ues distribution of general random walks on the symmetric group which is b
 ased on a generalization of ideas from free probability. These new tools w
 ere created in order to study random matrices invariant by the symmetric g
 roup and are based on a geometric study of partitions.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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