arXiv subjects

A. Guilloux

Publications and source records attributed to A. Guilloux.

2 recordsLinked to original sources

arXiv2013

Local rigidity for PGL(3,C)-representations of 3-manifold groups

Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by the gluing equations for PGL(3,C)-representations. In particular we prove local rigidity of the "geometric" representation in PGL(3,C), recovering a recent result of Menal-Ferrer and Porti. More generally we give a criterion for local rigidty of PGL(3,C)-representations and provide detailed analysis of the figure eight knot sister manifold exhibiting the different possibilities that can occur.

math.GT↗

arXiv2008

Adaptive estimation of the conditional intensity of marker-dependent counting processes

We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a non asymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly, we provide a short illustration of the way the estimator works in the context of conditional hazard estimation.

math.ST↗