Évènements

Barak-Erdös graphs are the directed acyclic version of Erdös-Rényi
random graphs : the vertex set is {1,…,n} and for each i<j with
probability p we add an edge directed from i to j, independently for
each pair i0 and is differentiable once but not twice at p=0. We also show
that the coefficients of the Taylor expansion at p=1 of C(p) are
integers, suggesting that C(p) is the generating function of some class
of combinatorial objects.

The neutron transport equation (NTE) describes the net movement of neutrons through an inhomogeneous fissile medium, such as a nuclear reactor. One way to derive the NTE is via the stochastic analysis of a spatial branching process. This approach has been known since the 1960/70s, however, since then, very little innovation in the literature has emerged through probabilistic analysis. In recent years, however, the nuclear power and nuclear regulatory industries have a greater need for a deep understanding the spectral properties of the NTE.

In this talk I will formally describe the dynamics of the so-called neutron branching process (NBP), along with an associated Feynman Kac representation. I will then discuss how the latter can be used to consider the long-term behaviour of the nuclear fission processes through both a Perron-Frobenius decomposition and a strong law of large numbers result.

In this talk I will present the problem of finding extremal potentials for the functional determinant of a one-dimensional Schrödinger operator defined on a bounded interval with Dirichlet boundary conditions. We consider potentials in a fixed $L^q$ space with $qgeq 1$. Functional determinants of Sturm-Liouville operators with smooth potentials or with potentials with prescribed singularities have been widely studied, I will present a short review of these results and will explain how to extend the definition of the functional determinant to potentials in $L^q$. The maximization problem turns out to be equivalent to a problem in optimal control. I will explain how we obtain existence and uniqueness of the maximizers. The results presented in the talk are join work with J-B. Caillau (UCDA, CNRS, Inria, LJAD) and P. Freitas (Lisboa).