Related papers: Brownian motion on stationary random manifolds

Brownian motion on manifolds with non-trivial diffusion coefficient can be constructed by stochastic development of Euclidean Brownian motions using the fiber bundle of linear frames. We provide a comprehensive study of paths for such…

We study collections of exact Lagrangian submanifolds respecting some uniform Riemannian bounds, which we equip with a metric naturally arising in symplectic topology (e.g. the Lagrangian Hofer metric or the spectral metric). We exhibit…

We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the…

We consider a single Brownian particle in a spatially symmetric, periodic system far from thermal equilibrium. This setup can be readily realized experimentally. Upon application of an external static force F, the average particle velocity…

In this paper, we study some intrinsic characterization of conformally compact manifolds. We show that, if a complete Riemannian manifold admits an essential set and its curvature tends to -1 at infinity in certain rate, then it is…

In this paper, we develop a way of analyzing the random dynamics of stochastic evolution equations with a non-dense domain. Such problems cover several types of evolution equations. We are particularly interested in evolution equations with…

In proving large deviation estimates, the lower bound for open sets and upper bound for compact sets are essentially local estimates. On the other hand, the upper bound for closed sets is global and compactness of space or an exponential…

We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary…

We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider…

We study harmonic and totally invariant measures in a foliated compact Riemannian manifold isometrically embedded in an Euclidean space. We introduce geometrical techniques for stochastic calculus in this space. In particular, using these…

We present a quasi-local version of the stability of the positive mass theorem. We work with the Brown--York quasi-local mass as it possesses positivity and rigidity properties, and therefore the stability of this rigidity statement can be…

Motivated by Segal's axiom of conformal field theory, we do a survey on geometrical random fields. We do a history of continuous random fields in order to arrive at a field theoretical analog of Klauder's quantization in Hamiltonian quantum…

For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the…

The Liouville property of a complete Riemannian manifold (i.e., the question whether there exist non-trivial bounded harmonic functions) attracted a lot of attention. For Cartan-Hadamard manifolds the role of lower curvature bounds is still…

Let B_1,B_2, ... be independent one-dimensional Brownian motions defined over the whole real line such that B_i(0)=0. We consider the nth iterated Brownian motion W_n(t)= B_n(B_{n-1}(...(B_2(B_1(t)))...)). Although the sequences of…

The stochastic rotational invariance of an integration by parts formula inspired by the Bismut approach to Malliavin calculus is proved in the framework of the Lie symmetry theory of stochastic differential equations. The non-trivial effect…

The interest in the concept of entropic forces has risen considerably since E. Verlinde proposed to interpret the force in Newton s second law and Gravity as entropic forces [1]. Brownian motion, the motion of a small particle (pollen)…

We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is…

We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for every group of automorphisms of bounded type of a rooted…

We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter $H\in(0,1)$. A general framework is constructed to make precise the notions of…