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

Contraction of Dark Matter Halos in Response to Condensation of Baryons

The cooling of baryons in the centers of dark matter halos leads to a more concentrated dark matter distribution. This effect has traditionally been calculated using the model of adiabatic contraction, which assumes spherical symmetry, while in hierarchical formation scenarios halos grow via multiple violent mergers. We test the adiabatic contraction model in high-resolution cosmological simulations and find that the dissipation of gas indeed increases the density of dark matter and steepens its radial profile compared to the case without cooling. Although the standard model systematically overpredicts the increase of dark matter density, a simple modification of the assumed invariant from M(r)r to M()r, where is the orbit-averaged particle position, reproduces the simulated profiles within 10%.Comment: 6 pages, invited talk at the XXI IAP Colloquium, Paris, July 200

Revisiting The First Galaxies: The effects of Population III stars on their host galaxies

We revisit the formation and evolution of the first galaxies using new hydrodynamic cosmological simulations with the ART code. Our simulations feature a recently developed model for H2 formation and dissociation, and a star formation recipe that is based on molecular rather than atomic gas. Here, we develop and implement a recipe for the formation of metal-free Population III stars in galaxy-scale simulations that resolve primordial clouds with sufficiently high density. We base our recipe on the results of prior zoom-in simulations that resolved the protostellar collapse in pre-galactic objects. We find the epoch during which Pop III stars dominated the energy and metal budget of the first galaxies to be short-lived. Galaxies which host Pop III stars do not retain dynamical signatures of their thermal and radiative feedback for more than 10^8 yr after the lives of the stars end in pair-instability supernovae, even when we consider the maximum reasonable efficiency of the feedback. Though metals ejected by the supernovae can travel well beyond the virial radius of the host galaxy, they typically begin to fall back quickly, and do not enrich a large fraction of the intergalactic medium. Galaxies with total mass in excess of 3 x 10^6 Msun re-accrete most of their baryons and transition to metal-enriched Pop II star formation.Comment: 13 pages, 9 figures, published in Ap