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UID:7023@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190607T110000
DTEND;TZID=Europe/Paris:20190607T120000
DTSTAMP:20241120T202651Z
URL:https://www.i2m.univ-amu.fr/evenements/on-the-circle-kahanes-gaussian-
 multiplicative-chaos-and-circular-random-matrices-match-reda-chhaibi/
SUMMARY:Reda Chhaibi (IMT\, Université Paul Sabatier Toulouse III): On the
  circle\, Kahane’s Gaussian Multiplicative Chaos and Circular Random Mat
 rices match - Reda Chhaibi
DESCRIPTION:Reda Chhaibi: In this talk\, I would like to advertise an equal
 ity between two objects from very different areas of mathematical physics.
  This bridges the Gaussian Multiplicative Chaos\, which plays an important
  role in certain conformal field theories\, and a reference model in rando
 m matrices.On the one hand\, in 1985\, J.P Kahane introduced a random meas
 ure called the Gaussian Multiplicative Chaos (GMC). Morally\, this is the 
 measure whose Radon-Nikodym derivative w.r.t to Lebesgue is the exponentia
 l of a log correlated Gaussian field. In the cases of interest\, this Gaus
 sian field is a Schwartz distribution but not a function. As such\, the co
 nstruction of GMC needs to bedone with care. In particular\, in 2D\, the G
 FF (Gaussian Free Field) is a randomSchwartz distribution because of the l
 ogarithmic singularity of the Green kernel in 2D. Here we are interested i
 n the 1D case on the circle. On the other hand\, it is known since Verblun
 sky (1930s) that a probability measure on the circle is entirely determine
 d by the coefficients appearing in the recurrence of orthogonal polynomial
 s. Furthermore\, Killip and Nenciu (2000s) have given a realization of the
  CBE\, an important model in random matrices\, thanks to random orthogonal
  polynomials of the circle. I will give the precise statement whose loose 
 form is CBE = GMC.\nWith J. Najnudel.\n[su_spacer size="10"]\n\nhttps://ar
 xiv.org/abs/1904.00578\n\n[su_spacer size="10"]
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Reda_Chhaibi.jpg
CATEGORIES:Séminaire,Probabilités
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DTSTART:20190331T030000
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