Ewens measures on compact groups and hypergeometric kernels

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure, these factors become independent random variables with explicit distributions. Beyond the known results on the orthogonal and unitary groups (O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family of probability changes analogous to the biassing in the Ewens sampling formula known for the symmetric group. Then we study the spectral properties of these measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The associated orthogonal polynomials give rise, as $n$ tends to infinity to a limit kernel at the singularity.Comment: New version of the previous paper "Hua-Pickrell measures on general compact groups". The article has been completely re-written (the presentation has changed and some proofs have been simplified). New references added

Galaxy filaments as pearl necklaces

Context. Galaxies in the Universe form chains (filaments) that connect groups and clusters of galaxies. The filamentary network includes nearly half of the galaxies and is visually the most striking feature in cosmological maps. Aims. We study the distribution of galaxies along the filamentary network, trying to find specific patterns and regularities. Methods. Galaxy filaments are defined by the Bisous model, a marked point process with interactions. We use the two-point correlation function and the Rayleigh Z-squared statistic to study how galaxies and galaxy groups are distributed along the filaments. Results. We show that galaxies and groups are not uniformly distributed along filaments, but tend to form a regular pattern. The characteristic length of the pattern is around 7 Mpc/h. A slightly smaller characteristic length 4 Mpc/h can also be found, using the Z-squared statistic. Conclusions. We find that galaxy filaments in the Universe are like pearl necklaces, where the pearls are galaxy groups distributed more or less regularly along the filaments. We propose that this well defined characteristic scale could be used to test various cosmological models and to probe environmental effects on the formation and evolution of galaxies.Comment: 8 pages, 9 figures, 1 table, accepted for publication in A&

A Type-Safe Model of Adaptive Object Groups

Services are autonomous, self-describing, technology-neutral software units that can be described, published, discovered, and composed into software applications at runtime. Designing software services and composing services in order to form applications or composite services requires abstractions beyond those found in typical object-oriented programming languages. This paper explores service-oriented abstractions such as service adaptation, discovery, and querying in an object-oriented setting. We develop a formal model of adaptive object-oriented groups which offer services to their environment. These groups fit directly into the object-oriented paradigm in the sense that they can be dynamically created, they have an identity, and they can receive method calls. In contrast to objects, groups are not used for structuring code. A group exports its services through interfaces and relies on objects to implement these services. Objects may join or leave different groups. Groups may dynamically export new interfaces, they support service discovery, and they can be queried at runtime for the interfaces they support. We define an operational semantics and a static type system for this model of adaptive object groups, and show that well-typed programs do not cause method-not-understood errors at runtime.Comment: In Proceedings FOCLASA 2012, arXiv:1208.432

Dependability Analysis of Control Systems using SystemC and Statistical Model Checking

Stochastic Petri nets are commonly used for modeling distributed systems in order to study their performance and dependability. This paper proposes a realization of stochastic Petri nets in SystemC for modeling large embedded control systems. Then statistical model checking is used to analyze the dependability of the constructed model. Our verification framework allows users to express a wide range of useful properties to be verified which is illustrated through a case study

Introduction to determinantal point processes from a quantum probability viewpoint

Determinantal point processes on a measure space X whose kernels represent trace class Hermitian operators on L^2(X) are associated to "quasifree" density operators on the Fock space over L^2(X).Comment: Contributed to the proceedings of the 26th Conference on Quantum Probability and Infinite Dimensional Analysi

Free fermions and the classical compact groups

There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of non-interacting free fermions with classical boundary conditions.Comment: 35 pages, 5 figures. Final versio