Projected Richardson varieties and affine Schubert varieties

Let $G$ be a complex quasi-simple algebraic group and $G/P$ be a partial flag variety. The projections of Richardson varieties from the full flag variety form a stratification of $G/P$. We show that the closure partial order of projected Richardson varieties agrees with that of a subset of Schubert varieties in the affine flag variety of $G$. Furthermore, we compare the torus-equivariant cohomology and $K$-theory classes of these two stratifications by pushing or pulling these classes to the affine Grassmannian. Our work generalizes results of Knutson, Lam, and Speyer for the Grassmannian of type $A$.Comment: 20 pages. To appear in Annales de l'institut fourie

Asymptotic properties of maximum likelihood estimators in models with multiple change points

Models with multiple change points are used in many fields; however, the theoretical properties of maximum likelihood estimators of such models have received relatively little attention. The goal of this paper is to establish the asymptotic properties of maximum likelihood estimators of the parameters of a multiple change-point model for a general class of models in which the form of the distribution can change from segment to segment and in which, possibly, there are parameters that are common to all segments. Consistency of the maximum likelihood estimators of the change points is established and the rate of convergence is determined; the asymptotic distribution of the maximum likelihood estimators of the parameters of the within-segment distributions is also derived. Since the approach used in single change-point models is not easily extended to multiple change-point models, these results require the introduction of those tools for analyzing the likelihood function in a multiple change-point model.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ232 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Status of the Zee-Babu model for neutrino mass and possible tests at a like-sign linear collider

We provide an updated scan of the allowed parameter space of the two-loop Zee-Babu model for neutrino mass. Taking into account most recent experimental data on $\mu\to e\gamma$ as well as the mixing angle $\theta_{13}$ we obtain lower bounds on the masses of the singly and doubly charged scalars of between 1 to 2 TeV, with some dependence on perturbativity and fine-tuning requirements. This makes the scalars difficult to observe at LHC with 14 TeV even with optimistic assumptions on the luminosity, and would require a multi-TeV linear collider to see the scalar resonances. We point out, however, that a sub-TeV linear collider in the like-sign mode may be able to observe lepton flavour violating processes such as $e^- e^- \to \mu^- \mu^-$ due to contact interactions induced by the doubly charged scalar with masses up to around 10 TeV. We investigate the possibility to distinguish the Zee-Babu model from the Higgs triplet model using such processes.Comment: 12 pages, 7 figure