Related papers: Octonionic Brownian Windings
The classification of the octonionic realizations of the one-dimensional extended supersymmetries is here furnished. These are non-associative realizations which, albeit inequivalent, are put in correspondence with a subclass of the already…
Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…
We prove asymptotic completeness in the energy space for the nonlinear Schrodinger equation posed on hyperbolic space in the radial case, in space dimension at least 4, and for any energy-subcritical, defocusing, power nonlinearity. The…
We study asymptotics of various Euclidean geometric phenomena as the dimension tend to infinity.
Evolution equations for the orientation distribution of axisymmetric particles in periodic flows are derived in the regime of small but non-zero Brownian rotations. The equations are based on a multiple time scale approach that allows fast…
The nature of space-time at high energy is an open question and the link between extra-dimensional theories with the physics of the Standard Model can not be established in a unique way. The compactification path is not unique and…
In the present paper we consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. They are called meridian surfaces…
In this article we establish some estimates related to the Gaussian densities and to Hermite polynomials in order to obtain an almost sure estimate for each term of the It\^{o}-Wiener expansion of the self-intersection local times of the…
We study the higher expansion properties of locally symmetric spaces, with a particular focus on octonionic hyperbolic manifolds. We show that codimension two minimal submanifolds of compact octonionic locally symmetric spaces must have…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
We consider an isothermal compressible fluid evolving on a cosmological background which may be either expanding or contracting toward the future. The Euler equations governing such a flow consist of two nonlinear hyperbolic balance laws…
We give explicit formulas and asymptotics for the distribution of the index of the Brownian loop in the following geometrical settings: the complex projective line from which two points have been removed; the complex hyperbolic line from…
The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and…
We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally…
We begin with a review and analytical construction of quantum Gaussian process (and quantum Brownian motions) in the sense of [25],[10] and others, and then formulate and study in details (with a number of interesting examples) a definition…
This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a Gaussian field $W$ on ${\mathbb{R}}_+\times{\mathbb{R}}$ which is white noise in time and function-valued…
The kinetic Brownian motion on the sphere bundle of a Riemannian manifold $M$ is a stochastic process that models a random perturbation of the geodesic flow. If $M$ is a orientable compact constantly curved surface, we show that in the…
We consider admissible random walks on hyperbolic graphs. For a given harmonic function on such a graph, we prove that asymptotic properties of non-tangential boundedness and non-tangential convergence are almost everywhere equivalent. The…
We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.
Asymptotic behavior of the one-dimensional Brownian motion in general random environments has been investigated by many researchers. However, many of the methods used in the argument are available only for the one-dimensional case. In this…