3,806 research outputs found
On the affine random walk on the torus
Let be a borelian probability measure on
. Define, for , a random walk starting at denoting for , where is an iid
sequence of law .
Then, we denote by the measure on
that is the image of by the map and for any
, we set
.
Bourgain, Furmann, Lindenstrauss and Mozes studied this random walk when
is concentrated on and this
allowed us to study, for any h\"older-continuous function on the torus, the
sequence when is not too well approximable by rational points.
In this article, we are interested in the case where is not
concentrated on
and we prove that, under assumptions on the group spanned by the support of
, the Lebesgue's measure on the torus is the only stationary
probability measure and that for any h\"older-continuous function on the
torus, converges exponentially fast to .
Then, we use this to prove the law of large numbers, a non-concentration
inequality, the functional central limit theorem and it's almost-sure version
for the sequence .
In the appendix, we state a non-concentration inequality for products of
random matrices without any irreducibility assumption
Environmental Protection, Producer Insolvency and Lender Liability
The present paper deals with some legal issues surrounding environmental protection, namely those issues concerning the liability of the different firms and individuals directly or indirectly involved in the generation of environment damaging accidents. We consider in particular the potential effects of extending a firm's liability in case of an environmental disaster to its lenders and financiers when the cost of this liability is too large in relation to the firm's assets. Such extended liability regimes exist or are considered in many countries. The most important case is the 1980/85 Comprehensive Environmental Response, Compensation and Liability Act (CERCLA) in the USA that led to an extensive jurisprudence over the last fifteen years. Nous traitons ici du cadre légal de la responsabilité directe des entreprises lors de désastres environnementaux et de l'extension de cette responsabilité aux prêteurs en cas de faillite de l'entreprise. De tels régimes existent ou sont à l'étude dans plusieurs pays. Le cas le plus connu est le Comprehensive Environmental Response, Compensation and Liability Act (CERCLA) de 1980/85 aux États-Unis et nous analysons les principaux cas de jurisprudence auxquels cette loi a donné lieu depuis 15 ans.Environment, Extended Lender Liability, CERCLA, Environnement, responsabilité, CERCLA
Exact Sparse Matrix-Vector Multiplication on GPU's and Multicore Architectures
We propose different implementations of the sparse matrix--dense vector
multiplication (\spmv{}) for finite fields and rings \Zb/m\Zb. We take
advantage of graphic card processors (GPU) and multi-core architectures. Our
aim is to improve the speed of \spmv{} in the \linbox library, and henceforth
the speed of its black box algorithms. Besides, we use this and a new
parallelization of the sigma-basis algorithm in a parallel block Wiedemann rank
implementation over finite fields
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