ar X iv : m at h / 05 10 30 5 v 1 [ m at h . PR ] 1 4 O ct 2 00 5 Recursive Partition Structures ∗

ar X iv : m at h / 05 10 24 8 v 1 [ m at h . O A ] 1 2 O ct 2 00 5 THE CORONA FACTORIZATION PROPERTY

The corona factorization property is a property with connections to extension theory, K-theory and the structure of C *-algebras. This paper is a short survey of the subject, together with some new results and open questions.

ar X iv : m at h / 05 04 37 3 v 1 [ m at h . Q A ] 1 9 A pr 2 00 5 Lax Operator for the Quantised Orthosymplectic

ar X iv : m at h / 05 04 08 2 v 4 [ m at h . D G ] 1 5 A pr 2 00 6 COMPLETE PROJECTIVE CONNECTIONS

The first examples of complete projective connections are uncovered: on surfaces, normal projective connections whose geodesics are all closed and embedded are complete. On manifolds of any dimension, normal projective connections induced from complete affine connections with slowly decaying positive Ricci curvature are complete.

ar X iv : m at h / 05 08 29 7 v 2 [ m at h . ST ] 3 O ct 2 00 5 CONVERGENCE OF ESTIMATORS IN LLS ANALYSIS

We establish necessary and sufficient conditions for consistency of estimators of mixing distribution in linear latent structure analysis.

ar X iv : m at h / 05 05 01 1 v 4 [ m at h . PR ] 5 J un 2 00 6 EXCHANGEABLE , GIBBS AND EQUILIBRIUM MEASURES FOR MARKOV

We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of “symmetric measure”: exchangeability and the Gibbs (or conformal) property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one dimensional case) exhibit a variety of spectral properties.