Quasi-semisimple elements

We study quasi-semisimple elements of disconnected reductive algebraic groups over an algebraically closed field. We describe their centralizers, define isolated and quasi-isolated quasi-semisimple elements and classify their conjugacy classes.Comment: This version: some corrections; index adde

Endomorphisms of Deligne-Lusztig varieties

This paper is a following to math.RT/0410454. For a finite group of Lie type we study the endomorphisms, commuting with the group action, of a Deligne-Lusztig variety associated to a regular element of the Weyl group. We state some general conjectures, in particular that the endomorphism algebra induced on the cohomology is a cyclotomic Hecke algebra, and prove them in some cases. On the way we also prove results on centralizers in braid groups

Garside and locally Garside categories

We define and give axioms for Garside and locally Garside categories. We give an application to Coxeter and Artin groups and Deligne-Lusztig varieties.Comment: We have fixed some errors pointed to us by E. Godelle and P. Dehornoy and added new results in section

Electricity Internal Market in the European Union: What to do next?

Like in the US, the EU “internal electricity market” remains unfinished and its construction can stall, fracturing into “national blocks” separated by permanent “border effects”. This is exactly what this paper seeks to avoid in the expected life of the current European Commission (2005-2009). It identifies the critical factors: national and EU market designs, industry structure and competition policy, deeper regional cooperation between TSOs and Regulators. It suggests 8 priority actions and 12 secondary improvements to sustain the dynamics of the construction of an EU set of open r egional markets with limited “border effects”, and explains the rationale for these recommendations

Maximum pseudo-likelihood estimator for nearest-neighbours Gibbs point processes

This paper is devoted to the estimation of a vector parametrizing an energy function associated to some "Nearest-Neighbours" Gibbs point process, via the pseudo-likelihood method. We present some convergence results concerning this estimator, that is strong consistency and asymptotic normality, when only a single realization is observed. Sufficient conditions are expressed in terms of the local energy function and are verified on some examples.Comment: 29 pages - 2 figure

Lifshitz tails estimate for the density of states of the Anderson model

We prove an upper bound for the (differentiated) density of states of the Anderson model at the bottom of the spectrum. The density of states is shown to exhibit the same Lifshitz tails upper bound as the integrated density of states

Resilience, reactivity and variability : A mathematical comparison of ecological stability measures

In theoretical studies, the most commonly used measure of ecological stability is resilience: ecosystems asymptotic rate of return to equilibrium after a pulse-perturbation $-$or shock. A complementary notion of growing popularity is reactivity: the strongest initial response to shocks. On the other hand, empirical stability is often quantified as the inverse of temporal variability, directly estimated on data, and reflecting ecosystems response to persistent and erratic environmental disturbances. It is unclear whether and how this empirical measure is related to resilience and reactivity. Here, we establish a connection by introducing two variability-based stability measures belonging to the theoretical realm of resilience and reactivity. We call them intrinsic, stochastic and deterministic invariability; respectively defined as the inverse of the strongest stationary response to white-noise and to single-frequency perturbations. We prove that they predict ecosystems worst response to broad classes of disturbances, including realistic models of environmental fluctuations. We show that they are intermediate measures between resilience and reactivity and that, although defined with respect to persistent perturbations, they can be related to the whole transient regime following a shock, making them more integrative notions than reactivity and resilience. We argue that invariability measures constitute a stepping stone, and discuss the challenges ahead to further unify theoretical and empirical approaches to stability.Comment: 35 pages, 7 figures, 2 table