Related papers: Brownian motion on stationary random manifolds
We consider random perturbations of a topologically transitive local diffeomorphism of a Riemannian manifold. We show that if an absolutely continuous ergodic stationary measures is expanding (all Lyapunov exponents positive), then there is…
In this PhD Thesis we investigate the geometry of random fields on compact Riemannian manifolds, in particular the two-dimensional sphere. In the first part, we characterize isotropic Gaussian fields on homogeneous spaces of a compact group…
We prove a sharp rate of convergence to stationarity for a natural random walk on a compact Riemannian manifold $(M,g)$. The proof includes a detailed study of the spectral theory of the associated operator.
The main result is a counterpart of the theorem of Monroe [\emph{Ann. Probability} \textbf{6} (1978) 42--56] for a geometric Brownian motion: A process is equivalent to a time change of a geometric Brownian motion if and only if it is a…
This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated…
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. We use Dirichlet form methods to construct…
We use the equivariant $\mu$-bubbles technique to prove that for any compact manifold $M^n$ with non-empty boundary, $n\in\{3,5,6\}$, the Yamabe invariant of $M^n$ is positive if and only if the Yamabe invariant of $M^n\times S^1$ is…
We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…
We obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on…
We study the polynomial entropy of the wandering part of any invertible dynamical system on a compact metric space. As an application we compute the polynomial entropy of Brouwer homeomorphisms (fixed point free orientation preserving…
We find obstructions to the existence of Einstein metrics of non-negative sectional curvature on a smooth closed simply connected manifold of any dimension. The results are achieved by combining the classical Morse theory of the loop space…
We study asymptotically compact nonautonomous dynamical systems given by abstract cocycles in Banach spaces. Our main assumptions are given by a squeezing property in a quadratic cone field (given by a family of indefinite quadratic…
We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that…
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent…
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold, and more generally of a finite simplicial complex, vanishes or is positive. In the first part of the article, we present…
We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and…
In this article we provide a proof of the so called absolute continuity theorem for random dynamical systems on $R^d$ which have an invariant probability measure. First we present the construction of local stable manifolds in this case.…
We develop Hamiltonian mechanics on Aristotelian manifolds, which lack local boost symmetry and admit absolute time and space structures. We construct invariant phase space dynamics, define free Hamiltonians, and establish a generalized…
We consider random walks in random environments on Z^d. Under a transitivity hypothesis that is much weaker than the customary ellipticity condition, and assuming an absolutely continuous invariant measure on the space of the environments,…