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Structure of large random hypergraphs

The theme of this paper is the derivation of analytic formulae for certain large combinatorial structures. The formulae are obtained via fluid limits of pure jump type Markov processes, established under simple conditions on the Laplace transforms of their Levy kernels. Furthermore, a related Gaussian approximation allows us to describe the randomness which may persist in the limit when certain parameters take critical values. Our method is quite general, but is applied here to vertex identifiability in random hypergraphs. A vertex v is identifiable in n steps if there is a hyperedge containing v all of whose other vertices are identifiable in fewer than n steps. We say that a hyperedge is identifiable if every one of its vertices is identifiable. Our analytic formulae describe the asymptotics of the number of identifiable vertices and the number of identifiable hyperedges for a Poisson random hypergraph on a set of N vertices, in the limit as N goes to infinity.Comment: Revised version with minor conceptual improvements and additional discussion. 32 pages, 5 figure

Are extremely luminous far-infrared galaxies the result of merging quasar cores

Extremely Luminous far-infrared galaxies (ELFs) are a class of galaxy discovered independently by several groups. The class is characterized by a quasar-like total luminosity (10(exp 11) to 10(exp 13) solar luminosity) which is radiated almost entirely in the far-infrared. It has been suggested that obscured quasar cores may be responsible for generating this luminosity. Here the author demonstrates that ELFs appear in several guises which can be characterized by the number of quasar cores they contain (zero, one or two). The author develops a unified model to account for these differences

Differential equation approximations for Markov chains

We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is emphasised. The general theory is illustrated in three examples: the classical stochastic epidemic, a population process model with fast and slow variables, and core-finding algorithms for large random hypergraphs.Comment: Published in at http://dx.doi.org/10.1214/07-PS121 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

Large deviations for the Yang-Mills measure on a compact surface

We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the Yang-Mills measures satisfy a large deviation principle with a rate function which is expressed in a simple and natural way in terms of the Yang-Mills energy

A thermal vacuum test optimization procedure

An analytical model was developed that can be used to establish certain parameters of a thermal vacuum environmental test program based on an optimization of program costs. This model is in the form of a computer program that interacts with a user insofar as the input of certain parameters. The program provides the user a list of pertinent information regarding an optimized test program and graphs of some of the parameters. The model is a first attempt in this area and includes numerous simplifications. The model appears useful as a general guide and provides a way for extrapolating past performance to future missions