Étude asymptotique d'une marche aléatoire centrifuge

battre la marche aléatoire en comptant ? †

Nous étudions le problème consistant à trouver une destination t dans un réseau, non fiable, grâce à un agent mobile. Chaque nœud du réseau peut donner un conseil quant au prochain sommet à visiter pour se rapprocher de t. Malheureusement, k nœuds, appelés menteurs, donnent de mauvais conseils. Il est connu que pour un graphe G de n sommets et de degré maximum ∆ ≥ 3, atteindre une cible à dista...

G-Réseaux dans un environnement aléatoire

Extending DUNE: The dune-xt modules

We present our effort to extend and complement the core modules of the Distributed and Unified Numerics Environment DUNE (http://dune-project.org) by a well tested and structured collection of utilities and concepts. We describe key elements of our four modules dune-xt-common, dune-xt-grid, dune-xt-la and dune-xt-functions, which aim at further enabling the programming of generic algorithms wit...

Hauteur asymptotique des points de Heegner

Geometric intuition suggests that the Néron-Tate height of Heegner points on a rational elliptic curve E should be asymptotically governed by the degree of its modular parametrisation. In this paper, we show that this geometric intuition asymptotically holds on average over a subset of discriminants. We also study the asymptotic behaviour of traces of Heegner points on average over a subset of ...

Non Unitary Random Walks

Motivated by the recent refutation of information loss paradox in black hole by Hawking, we investigate the new concept of non unitary random walks. In a non unitary random walk, we consider that the state 0, called the black hole, has a probability weight that decays exponentially in e−λt for some λ > 0. This decaying probabilities affect the probability weight of the other states, so that the...