Two examples of non strictly convex large deviations

We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex large deviations. For one of these examples, we show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied.Comment: 11 page

Hint of Lepton Flavour Non-Universality in BB Meson Decays

The LHCb collaboration has recently presented their result on R_K = BR(B+ -> K+ mu+ mu-)/ BR(B+ -> K+ e+ e-) for the dilepton invariant mass bin m_{ll}^2 = 1-6 GeV^2 (l = mu, e). The measurement shows an intriguing 2.6 sigma deviation from the Standard Model (SM) prediction. In view of this, we study model independent New Physics (NP) explanations of R_K consistent with other measurements involving b -> s l l transition, relaxing the assumption of lepton universality. We perform a Bayesian statistical fit to the NP Wilson Coefficients and compare the Bayes Factors of the different hypotheses in order to quantify their goodness-of-fit. We show that the data slightly favours NP in the muon sector over NP in the electron sector.Comment: Final version, to appear in JHE

Spacelike hypersurfaces in standard static spacetimes

In this work we study spacelike hypersurfaces immersed in spatially open standard static spacetimes with complete spacelike slices. Under appropriate lower bounds on the Ricci curvature of the spacetime in directions tangent to the slices, we prove that every complete CMC hypersurface having either bounded hyperbolic angle or bounded height is maximal. Our conclusions follow from general mean curvature estimates for spacelike hypersurfaces. In case where the spacetime is a Lorentzian product with spatial factor of nonnegative Ricci curvature and sectional curvatures bounded below, we also show that a complete maximal hypersurface not intersecting a spacelike slice is itself a slice. This result is obtained from a gradient estimate for parametric maximal hypersurfaces.Comment: 50 page