A phase transition for the heights of a fragmentation tree

We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behaviours of the shattering times, defined as the first instants when all the blocks of the partition process have cardinality less than a fixed integer. Our results may be applied to the study of certain random split trees

Martingales in self-similar growth-fragmentations and their connections with random planar maps

The purpose of the present work is twofold. First, we develop the theory of general self-similar growth-fragmentation processes by focusing on martingales which appear naturally in this setting and by recasting classical results for branching random walks in this framework. In particular, we establish many-to-one formulas for growth-fragmentations and define the notion of intrinsic area of a growth-fragmentation. Second, we identify a distinguished family of growth-fragmentations closely related to stable L\'evy processes, which are then shown to arise as the scaling limit of the perimeter process in Markovian explorations of certain random planar maps with large degrees (which are, roughly speaking, the dual maps of the stable maps of Le Gall & Miermont. As a consequence of this result, we are able to identify the law of the intrinsic area of these distinguished growth-fragmentations. This generalizes a geometric connection between large Boltzmann triangulations and a certain growth-fragmentation process, which was established in arXiv:1507.02265 .Comment: 50 pages, 5 figures. Final version: to appear in Probab. Theory Related Field

Simulating anthropogenic impacts to bird communities in tropical rain forests

We used an aggregated modelling approach to simulate the impacts ofanthropogenic disturbances on the long-term dynamics of faunal diversityin tropical rain forests. We restricted our study to bird communities eventhough the approach is more general. We developed a model calledBIODIV which simulated the establishment of hypothetical bird speciesin a forest. Our model was based on the results of a simple matrix modelwhich calculated the spatio-temporal dynamics of a tropical rain forest inMalaysia. We analysed the establishment of bird species in a secondaryforest succession and the impacts of 60 different logging scenarios on thediversity of the bird community. Of the three logging parameters(cycle length, method, intensity), logging intensity had the most servereimpact on the bird community. In the worst case the number of bird specieswas reduced to 23% of the species richness found in a primary forest

Dismantling sparse random graphs

We consider the number of vertices that must be removed from a graph G in order that the remaining subgraph has no component with more than k vertices. Our principal observation is that, if G is a sparse random graph or a random regular graph on n vertices with n tending to infinity, then the number in question is essentially the same for all values of k such that k tends to infinity but k=o(n).Comment: 7 page

Carbon-Enhanced Metal-Poor Stars, the Cosmic Microwave Background, and the Stellar IMF in the Early Universe

The characteristic mass of stars at early times may have been higher than today owing to the cosmic microwave background (CMB). This study proposes that (1) the testable predictions of this "CMB-IMF" hypothesis are an increase in the fraction of carbon-enhanced metal-poor (CEMP) stars with declining metallicity and an increase from younger to older populations at a single metallicity (e.g. disk to halo), and (2) these signatures are already seen in recent samples of CEMP stars and can be better tested with anticipated data. The expected spatial variation may explain discrepancies of CEMP frequency among published surveys. The ubiquity and time dependence of the CMB will substantially alter the reconstruction of star formation histories in the Local Group and early Universe.Comment: 7 pages emulateapj format, three figures, accepted for ApJ Letter

Statistical aspects of random fragmentations

AbstractThree random fragmentation of an interval processes are investigated. For each of them, there is a splitting probability and a probability not to split at each step of the fragmentation process whose overall effect is to stabilize the global number of splitting events. Some of their statistical features are studied in each case among which fragments’ size distribution, partition function, structure of the underlying random fragmentation tree, occurrence of a phase transition. In the first homogeneous model, splitting probability does not depend on fragments’ size at each step. In the next two fragmentation models, splitting probability is fragments’ length dependent. In the first such models, fragments further split with probability one if their sizes exceed some cutoff value only; in a second model considered, splitting probability of finite-size objects is assumed to increase algebraically with fragments’ size at each step. The impact of these dependencies on statistical properties of the resulting random partitions are studied. Several examples are supplied

Single electrons from heavy-flavor mesons in relativistic heavy-ion collisions

We study the single electron spectra from $D-$ and $B-$meson semileptonic decays in Au+Au collisions at $\sqrt{s_{\rm NN}}=$200, 62.4, and 19.2 GeV by employing the parton-hadron-string dynamics (PHSD) transport approach that has been shown to reasonably describe the charm dynamics at RHIC and LHC energies on a microscopic level. In this approach the initial heavy quarks are produced by using the PYTHIA which is tuned to reproduce the FONLL calculations. The produced heavy quarks interact with off-shell massive partons in QGP with scattering cross sections which are calculated in the dynamical quasi-particle model (DQPM). At energy densities close to the critical energy density the heavy quarks are hadronized into heavy mesons through either coalescence or fragmentation. After hadronization the heavy mesons interact with the light hadrons by employing the scattering cross sections from an effective Lagrangian. The final heavy mesons then produce single electrons through semileptonic decay. We find that the PHSD approach well describes the nuclear modification factor $R_{\rm AA}$ and elliptic flow $v_2$ of single electrons in d+Au and Au+Au collisions at $\sqrt{s_{\rm NN}}=$ 200 GeV and the elliptic flow in Au+Au reactions at $\sqrt{s_{\rm NN}}=$ 62.4 GeV from the PHENIX collaboration, however, the large $R_{\rm AA}$ at $\sqrt{s_{\rm NN}}=$ 62.4 GeV is not described at all. Furthermore, we make predictions for the $R_{\rm AA}$ of $D-$mesons and of single electrons at the lower energy of $\sqrt{s_{\rm NN}}=$ 19.2 GeV. Additionally, the medium modification of the azimuthal angle $\phi$ between a heavy quark and a heavy antiquark is studied. We find that the transverse flow enhances the azimuthal angular distributions close to $\phi=$ 0 because the heavy flavors strongly interact with nuclear medium in relativistic heavy-ion collisions and almost flow with the bulk matter.Comment: 20 pages, 20 figure