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UID:news1021@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20200216T193239
DTSTART;TZID=Europe/Zurich:20191218T110000
SUMMARY:Seminar in probability theory: Debapratim Banerjee (ISI\, Kolkata)
DESCRIPTION:We consider a spin system containing pure two spin Sherrington-
 Kirkpatrick Hamiltonian with Curie-Weiss interaction. The model where the 
 spins are spherically symmetric was considered by Baik and Lee and Baik et
  al. which shows a two dimensional phase transition with respect to temper
 ature and the coupling constant. In this paper we prove a result analogous
  to Baik and Lee in the “paramagnetic regime” when the spins are i.i.d
 . Rademacher. We prove the free energy in this case is asymptotically Gaus
 sian and can be approximated by a suitable linear spectral statistics. Unl
 ike the spherical symmetric case the free energy here can not be written a
 s a function of the eigenvalues of the corresponding interaction matrix. T
 he method in this paper relies on a dense sub-graph conditioning technique
  introduced by Banerjee . The proof of the approximation by the linear spe
 ctral statistics part is close to Banerjee and Ma.\\r\\nhttps://probabilit
 y.dmi.unibas.ch/seminar.html [https://probability.dmi.unibas.ch/seminar.ht
 ml]
X-ALT-DESC:<table><tbody><tr><td colspan="2">We consider a spin system cont
 aining pure two spin Sherrington-Kirkpatrick Hamiltonian with Curie-Weiss 
 interaction. The model where the spins are spherically symmetric was consi
 dered by Baik and Lee and Baik et al. which shows a two dimensional phase 
 transition with respect to temperature and the coupling constant. In this 
 paper we prove a result analogous to Baik and Lee in the “paramagnetic r
 egime” when the spins are i.i.d. Rademacher. We prove the free energy in
  this case is asymptotically Gaussian and can be approximated by a suitabl
 e linear spectral statistics. Unlike the spherical symmetric case the free
  energy here can not be written as a function of the eigenvalues of the co
 rresponding interaction matrix. The method in this paper relies on a dense
  sub-graph conditioning technique introduced by Banerjee . The proof of th
 e approximation by the linear spectral statistics part is close to Banerje
 e and Ma.</td></tr><tr></tr></tbody></table>\n<p><a href="https://probabil
 ity.dmi.unibas.ch/seminar.html">https://probability.dmi.unibas.ch/seminar.
 html</a></p>
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