Coutin, Laure Decreusefond, Laurent

The original Donsker theorem says that a standard random walk converges in distribution to a Brownian motion in the space of continuous functions. It has recently been extended to enriched random walks and enriched Brownian motion. We use the Stein-Dirichlet method to precise the rate of this convergence in the topology of fractional Sobolev spaces...

Delavoie, Franck Soldan, Vanessa Rinaldi, Dana Dauxois, Jean-Yves Gleizes, Pierre-Emmanuel

Determining the path of single ribonucleoprotein (RNP) particles through the 100 nm-wide nuclear pore complex (NPC) by fluorescence microscopy remains challenging due to resolution limitation and RNP labeling constraints. By using high-pressure freezing and electron tomography, here we captured snapshots of the translocation of native RNP particles...

Labbé, Cyril

We construct the continuous Anderson hamiltonian on $(-L,L)^d$ driven by a white noise and endowed with either Dirichlet or periodic boundary conditions. Our construction holds in any dimension $d\le 3$ and relies on the theory of regularity structures: it yields a self-adjoint operator in $L^2\big((-L,L)^d\big)$ with pure point spectrum. In $d\ge ...

Bostan, Alin Marynych, Alexander Raschel, Kilian

Let $L_n(k)$ denote the least common multiple of $k$ independent random integers uniformly chosen in $\{1,2,\ldots ,n\}$. In this note, using a purely probabilistic approach, we derive a criterion for the convergence in distribution as $n\to\infty$ of $\frac{f(L_n(k))}{n^{rk}}$ for a wide class of multiplicative arithmetic functions $f$ with polyno...

Lejay, Antoine Lenôtre, Lionel Pichot, Géraldine

We present a new Monte Carlo algorithm to simulate diffusion processes in presence of discontinuous convective and diffusive terms. The algorithm is based on the knowledge of close form analytic expressions of the resolvents of the diffusion processes which are usually easier to obtain than close form analytic expressions of the density. In the par...

Franceschi, Sandro Raschel, Kilian

For Brownian motion in a (two-dimensional) wedge with negative drift and oblique reflection on the axes, we derive an explicit formula for the Laplace transform of its stationary distribution (when it exists), in terms of Cauchy integrals and generalized Chebyshev polyno-mials. To that purpose we solve a Carleman-type boundary value problem on a hy...

Monmarché, Pierre Weisman, Jeremy Lagardère, Louis Piquemal, Jean-Philip

Ehrlacher, Virginie Lelièvre, Tony Monmarché, Pierre

Fang, Shizan Qian, Zhongmin

We will consider the Navier-Stokes equation on a Riemannian manifold M with Ricci tensor bounded below, the involved Laplacian operator is De Rham-Hodge Laplacian. The novelty of this work is to introduce a family of connections which are related to solutions of the Navier-Stokes equation, so that vorticity and helicity can be linked through the as...

Berglund, Nils Kuehn, Christian

Lemma 4.8 in the article [Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions, Electronic J. Probability 21 (18):1-48 (2016), hal-01141380] contains a mistake, which implies a weaker regularity estimate than the one stated in Proposition 4.11. This does not affect the proof of Theorem 2.1, but Theorems 2.2 a...