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SUMMARY:Zechuan Zheng (ENS Paris)
DTSTART:20211021T144500Z
DTEND:20211021T163000Z
DTSTAMP:20260423T022838Z
UID:LIJC/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LIJC/50/">Ma
 trix bootstrap revisited</a>\nby Zechuan Zheng (ENS Paris) as part of Lond
 on Integrability Journal Club\n\n\nAbstract\nMatrix bootstrap is a new met
 hod for the numerical study of (multi)-matrix models in the planar limit\,
  using loop equations for moments of distribution (Ward identities and fac
 torization of traces at infinite N). The lack of information associated wi
 th the use of only a finite number of lower moments is supplemented by the
  conditions of positivity of the correlation matrix. The numerical solutio
 n of loop equations and these conditions leads to inequalities for the low
 est moments\, which rapidly converge to exact values ​​with an increas
 e in the number of used moments. In our work https://arxiv.org/pdf/2108.04
 830.pdf\, the method was tested on the example of the standard one-matrix 
 model\, as well as on the case of an “unsolvable” 2-matrix model with 
 the interaction $tr[A\, B]^2$ and with quartic potentials. We propose a si
 gnificant improvement of original H.Lin’s proposal for matrix bootstrap 
 by introducing the relaxation procedure: we replace the non-convex\, non-l
 inear loop equations by convex inequalities. The results look quite convin
 cing and matrix bootstrap seems to be an interesting alternative to the Mo
 nte Carlo method. For example\, for $\\langle tr A^2 \\rangle$\, the preci
 sion reaches 6 digits (with modest computer resources). I will discuss the
  prospects for applying the method in other\, physically interesting syste
 ms.\n
LOCATION:https://researchseminars.org/talk/LIJC/50/
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