Recherche

Julien Bureaux

Docteur en mathématiques depuis décembre 2015, j'ai préparé ma thèse au sein du laboratoire MODAL'X sous la direction de Nathanaël Enriquez.

Mes travaux portent sur l'application de méthodes probabilistes à l'étude asymptotique d'objets combinatoires tels que les partitions entières et à la géométrie convexe discrète.

Publications

  1. Partitions of large unbalanced bipartites.
    Math. Proc. Cambridge. Philos. Soc. 157 (2014), no. 3, 469-487

    We compute the asymptotic behaviour of the number of partitions of large vectors \((n_1, n_2)\) of \(\mathbb{Z}_+^2\) in the critical regime \(n_1 \asymp \sqrt{n_2}\) and in the subcritical regime \(n_1 = o(\sqrt{n_2})\). This work completes the results established in the fifties by Auluck, Nanda and Wright.

    Article (pdf), HAL, arXiv, Journal

  2. Convex lattice polygonal lines with a constrained number of vertices avec Nathanaël Enriquez.
    À paraître dans Israel J. Math. (2016)

    A detailed combinatorial analysis of planar convex lattice polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a limit shape when the number of vertices is constrained.

    HAL, arXiv.

  3. On the number of lattice convex chains avec Nathanaël Enriquez.
    Discrete Anal. 2016, Paper No. 19, 15p.

    An asymptotic formula is presented for the number of planar lattice convex polygonal lines joining the origin to a distant point of the diagonal. The formula involves the non-trivial zeros of the zeta function and leads to a necessary and sufficient condition for the Riemann Hypothesis to hold.

    HAL, arXiv, Journal.

    OEIS sequence A267862.

  4. Convex cones, integral zonotopes, limit shape avec Imre Bárány et Ben Lund.
    Prépublication (2016)

    This paper is about integral zonotopes. It is proven that large zonotopes in a convex cone have a limit shape, meaning that, after suitable scaling, the overwhelming majority of the zonotopes are very close to a fixed convex set. Several combinatorial properties of large zonotopes are established.

    HAL, arXiv.

  5. The probability that two random integers are coprime avec Nathanaël Enriquez.
    À paraître dans Math. Nachr. (2017)

    An equivalence is proven between the Riemann Hypothesis and the speed of convergence to \(1/\zeta(2)\) of the probability that two independent random variables following the same geometric distribution are coprime integers, when the parameter of the distribution goes to 0.

    HAL, arXiv.

Travaux plus anciens

Quelques documents rédigés avant ma thèse :