Neeraja Sahasrabudhe: Covariance realization problem for spin systems
Neeraja Sahasrabudhe, University of Padova.
Time: Thu 2012-10-11 14.15
Location: Room 3721, Lindstedtsvägen 25, 7th floor, Department of Mathematics, KTH
We consider a covariance realization problem for spin systems. The necessary and sufficient
conditions for a covariance matrix of order n \leq 4 to be a spin
covariance matrix are already known. We give a fairly general and large set of inequalities,
parametrized by \lambda \in R^{n^2}, that are necessary and sufficient for any
n. We also give a minimal set of necessary and sufficient conditions for n = 5, 6. Finally, we
discuss methods to explicitly find the measure that realizes the given spin correlations (if they
are feasible). We give a deterministic algorithm as well as a stochastic version of the same
algorithm to find the measure explicitly.This is a joint work with Paolo Dai Pra and Michele Pavon.