Multi--dimensional Cosmological Radiative Transfer with a Variable Eddington Tensor Formalism

We present a new approach to numerically model continuum radiative transfer based on the Optically Thin Variable Eddington Tensor (OTVET) approximation. Our method insures the exact conservation of the photon number and flux (in the explicit formulation) and automatically switches from the optically thick to the optically thin regime. It scales as N logN with the number of hydrodynamic resolution elements and is independent of the number of sources of ionizing radiation (i.e. works equally fast for an arbitrary source function). We also describe an implementation of the algorithm in a Soften Lagrangian Hydrodynamic code (SLH) and a multi--frequency approach appropriate for hydrogen and helium continuum opacities. We present extensive tests of our method for single and multiple sources in homogeneous and inhomogeneous density distributions, as well as a realistic simulation of cosmological reionization.Comment: Accepted for publication in New Astronomy. Color GIF versions of figures 6, 7, 8, and 11 are available at http://casa.colorado.edu/~gnedin/PAPERPAGES/rt.htm

A Species Sampling Model with Finitely many Types

A two-parameter family of exchangeable partitions with a simple updating rule is introduced. The partition is identified with a randomized version of a standard symmetric Dirichlet species-sampling model with finitely many types. A power-like distribution for the number of types is derived

Coherent random permutations with record statistics

Random permutations with distribution conditionally uniform given the set of record values can be generated in a unified way, coherently for all values of $n$. Our central example is a two-parameter family of random permutations that are conditionally uniform given the counts of upper and lower records. This family interpolates between two versions of Ewens' distribution. We discuss characterisations of the conditionally uniform permutations, their asymptotic properties, constructions and relations to random partitions.Comment: 17 page

Constrained exchangeable partitions

For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown