Statut  Confirmé 
Série  IPHTPHM 
Domaines  mathph 
Date  Lundi 1 Octobre 2018 
Heure  11:00 
Institut  IPHT 
Salle  Salle Claude Itzykson, Bât. 774 
Nom de l'orateur  Ivan Dornic 
Prenom de l'orateur  
Addresse email de l'orateur  
Institution de l'orateur  SPEC, CEA/Saclay 
Titre  A tale of Pfaffian persistence tails told by a Painlevé VI transcendent 
Résumé  We identify the persistence probability for the spin located at the origin of a halfspace magnetized GlauberIsing chain as a Fredholm Pfaffian gap probability generating function with a sechkernel. This is then recast as a taufunction for a certain Painlevé VI transcendent  a sort of exact Kramers' formula for the associated explicitely timedependent Hamiltonian  where the persistence exponent emerges as an asymptotic decay rate. By a known yet remarkable correspondence that relates Painlevé equations to Bonnet surfaces, the persistence probability has also a geometric meaning Ã la GaussBonnet in terms of the intrinsic curvature of the underlying surface. Since the same sechkernel with an underlying Pfaffian structure shows up in a variety of Gaussian firstpassage problems, our Painlevé VI characterization appears as a universal probability distribution akin to the famous Painlevé II TracyWidom laws. Its tail behavior in the magnetizationsymmetric case allows in particular to recover the exact value 3/16 for the persistence exponent of a 2d diffusing random field, as found very recently by Poplavskyi and Schehr (arXiv:1806.11275). Due to its topological origin, this value should constitute the superuniversal persistence exponent for the coarsening of a nonconserved scalar order parameter in two space dimensions. 
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