Status  Confirmed 
Seminar Series  SEMLPTMC 
Subjects  condmat.meshall 
Date  Monday 16 September 2019 
Time  10:45 
Institute  LPTMC 
Seminar Room  Jussieu, tower 1312, room 523 
Speaker's Last Name  Dornic 
Speaker's First Name  Ivan 
Speaker's Email Address  ivan [dot] dornic [at] cea [dot] fr 
Speaker's Institution  SPEC CEA Saclay & LPTMC 
Title  A tale of Pfaffian persistence tails told by a Painlevé VI transcendent 
Abstract  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 ŕ 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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