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SUMMARY:On a perceptron version of the Generalized Random Energy Model - B
 olthausen\, E (Zrich)
DTSTART:20081215T113000Z
DTEND:20081215T123000Z
UID:TALK15727@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider a macroscopically large family of cavity variables
  whose covariances are given in a hierarchical way\, similar to Derrida's 
 generalized random energy model. The model is similar to the perceptron wh
 ere the cavity variables have a covariance structure given by the overlaps
  of two spin configurations. We therefore call the model a perceptron vers
 ion of the GREM. In contrast to the GREM itself\, the model has a rich asy
 mptotic behavior. The free energy is given by a formula which closely rese
 mbles the Parisi formula for the SK model. The limiting ultrametric struct
 ure depends in a complicated way on the the temperature parameter. Also\, 
 in contrast to the GREM\, the model has the chaos property (in temperature
 ).
LOCATION:Seminar Room 1\, Newton Institute
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