Category: Point processes

Si l'on suivait les voies ferroviaires, qui aurait le pied marin ?

Stein, Rubinstein, Malliavin, Poisson

One of many advantages of the Stein’s method is its versatility. It can be applied to prove convergence to Gaussian random variables or processes as well as to Poisson random variables or point processes. In this new paper, we investigate this last aspect showing that some multi-points transformation of some point processes lead to a…

Geometry of wireless systems

A few years ago, browsing the notices of the AMS, I found an article by R. Ghrist and V. de Silva about topological algebra used for detecting coverage problem. Barely stated, the difficulty is as follows: Consider a set of sensors, each of which detecting intrusion in a region around itself; how can we be…

Stein’s method in infinite dimension

The Stein method is a generic method to evaluate distance between probability measures. It is often applied to prove convergence towards Gaussian or Poisson distribution. Its principle is summarized by the following graph. To compare the probability measures (m) and (m_beta), one constructs a Markov process which is ergodic, whose stationary distribution is (m_beta) and…

Edgeworth series with error bounds

Edgeworth series refine the central limit theorem. Playing with Stein method and Malliavin calculus, we can retrieve Edgeworth series and precise the error bounds. http://hal.archives-ouvertes.fr/hal-00685272 The infinite dimension version is under preparation.

Random homology and wireless networks

Algebraic topology has been extensively and successfully used in image processing for a long time. In telecommunication networks, it can be used to verify that a zone in the plane is fully covered by a set of base stations with a few informations on their relative locations. In this article, we compute some of the…

Determinantal processes

Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion. These processes are thus very far from the uncorrelated situation encountered in Poisson models. Quasi-invariance In the linked paper, we establish a quasi-invariance result : we show that if atoms…