相关论文: Transportation to random zeroes by the gradient fl…
The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of solutions to the associated ODEs, which no longer satisfy…
In this paper we define distance expanding random dynamical systems. We develop the appropriate thermodynamic formalism of such systems. We obtain in particular the existence and uniqueness of invariant Gibbs states, the appropriate…
We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study…
For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
Ray flow methods are an efficient tool to estimate vibro-acoustic or electromagnetic energy transport in complex domains at high-frequencies. Here, a Petrov-Galerkin discretization of a phase-space boundary integral equation for…
We consider the branching random walk on the real line where the underlying motion is of a simple random walk and branching is at least binary and at most decaying exponentially in law. It is well known that the normalized empirical measure…
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…
We study a random bisection problem where an initial interval of length x is cut into two random fragments at the first stage, then each of these two fragments is cut further, etc. We compute the probability P_n(x) that at the n-th stage,…
A method is presented for the computation of the one-loop effective action at finite temperature and density. The method is based on an expansion in the number of spatial covariant derivatives. It applies to general background field…
We introduce a transport-majorization argument that establishes a majorization in the convex order between two densities, based on control of the gradient of a transportation map between them. As applications, we give elementary derivations…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise…
Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…
This paper is concerned with sampling from probability distributions $\pi$ on $\mathbb{R}^d$ admitting a density of the form $\pi(x) \propto e^{-U(x)}$, where $U(x)=F(x)+G(Kx)$ with $K$ being a linear operator and $G$ being…
For Laplacian models in dimension $(1+1)$ we derive sample path large deviations for the profile height function, that is, we study scaling limits of Gaussian integrated random walks and Gaussian integrated random walk bridges perturbed by…
Using a composite fermion picture, we study the lateral transport between two two-dimensional electron gases, at filling factor 1/2, separated by a potential barrier. In the mean field approximation, composite fermions far from the barrier…
Safety is a critical concern for the success of urban air mobility, especially in dynamic and uncertain environments. This paper proposes a path planning algorithm based on RRT in conjunction with chance constraints in the presence of…
Exponential, and not Gaussian, decay of probability density functions was studied by Laplace in the context of his analysis of errors. Such Laplace propagators for the diffusive motion of single particles in disordered media were recently…