Statut  Confirmé 
Série  MATHIHES 
Domaines  hepth 
Date  Mercredi 13 Septembre 2017 
Heure  16:30 
Institut  IHES 
Salle  Amphithéâtre Léon Motchane 
Nom de l'orateur  Lis 
Prenom de l'orateur  Marcin 
Addresse email de l'orateur  
Institution de l'orateur  Cambridge & IHES 
Titre  Total positivity in planar spin systems 
Résumé  Totally positive matrices are characterized by having all their minors positive. They appear in various areas of physics and mathematics, including oscillations in mechanical systems, quantum groups, and algebraic geometry. It has been known since the work of Fomin that the twopoint correlations functions of the twodimensional Gaussian free field satisfy total positivity. I will present an analogous result for the correlations of the planar Ising model. The idea is to prove that determinants of such correlations have interpretations in terms of probabilities of events in the random current model. A natural open question is to identify all planar totally positive spin systems. 
Numéro de preprint arXiv  
Commentaires  Séminaire de probabilités et physique statistique de l’IHES (Organisateur : Hugo DUMINILCOPIN) 
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