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Lyons and Sullivan have shown how to discretize harmonic functions on a Riemannian manifold $M$ whose Brownian motion satisfies a certain recurrence property called $\ast$-recurrence. We study analogues of this discretization for tensor…
Wave turbulence is the study of the long-time statistical behaviour of equations describing a set of weakly non-linear interacting waves. Such a theory, which has a natural asymptotic closure, allows us to probe the nature of turbulence…
We establish an integral test describing the exact cut-off between recurrence and transience for normally reflected Brownian motion in certain unbounded domains in a class of warped product manifolds. Besides extending a previous result by…
In this paper we investigate the Quantum Brownian motion of a point particle induced by quantum vacuum fluctuations of a massless scalar field in (3 + 1)-dimensional Minkowski spacetime with distinct conditions (Dirichlet, Neumann, mixed…
The effective action for quantum gravity coupled to matter contains corrections arising from the functional measure. We analyse the effect of such corrections for anisotropic self-gravitating compact objects described by means of the…
Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess,…
The aim of this paper is to study the asymptotic behaviour of a class of self- attracting motions on R^d . Using stochastic approximation methods, these processes have already been studied by Bena\"im, Ledoux and Raimond (2002) in a compact…
The goal of this paper is to propose a theoretical framework to study homogeneous and isotropic turbulence in a viscoelastic fluid, regarded as a perturbation of a Newtonian incompressible fluid, where the fluid relaxation time, or else the…
In this paper it is implemented how to make compatible the boundary conditions and the gauge fixing conditions for complex general relativity written in terms of Ashtekar variables using the Henneaux-Teitelboim-Vergara approach. Moreover,…
In this paper, we study the stochastic homogenization for a class of symmetric random walks in random conductance model, whose one-step transition probability from $x$ to $y$ is proportional to $|x-y|^{-d-2}$. As the associated jumping…
We consider a family of Riemannian manifolds M such that for each unit speed geodesic gamma of M there exists a distinguished bijective correspondence L between infinitesimal translations along gamma and infinitesimal rotations around it.…
We present a new simple method for rounding a semidefinite programming relaxation of a constraint satisfaction problem. We apply it to the problem of approximate angular synchronization. Specifically, we are given directed distances on a…
Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific…
In this paper we study a parametric class of stochastic processes to model both fast and slow anomalous diffusion. This class, called generalized grey Brownian motion (ggBm), is made up off self-similar with stationary increments processes…
We construct a model of Brownian Motion on a pseudo-Riemannian manifold associated with general relativity. There are two aspects of the problem: The first is to define a sequence of stopping times associated with the Brownian "kicks" or…
We extend Teichmueller dynamics to a flow on the total space of a flat bundle of deformation spaces of representations of the fundamental group of a fixed surface S in a Lie group G. The resulting dynamical system is a continuous version of…
In this monograph, we construct and study a sigma-finite measure on continuous functions from R_+ to R, strongly related to many probability measures obtained by penalisation of Brownian motion, i.e. as limits of probabilities which are…
We study the dynamics of a quantum or classical particle in a two-dimensional rotating anisotropic harmonic potential. By a sequence of symplectic transformations for constant rotation velocity we find uncoupled normal generalized…
We study holographic isotropisation of homogeneous, strongly coupled, non-Abelian plasmas in Gauss-Bonnet gravity with a negative cosmological constant. We focus on small values of the Gauss-Bonnet coupling parameter $\lambda_{GB}$ and…
We prove the homogenization of a class of one-dimensional viscous Hamilton-Jacobi equations with random Hamiltonians that are nonconvex in the gradient variable. Due to the special form of the Hamiltonians, the solutions of these PDEs with…