arXiv research

Study on massless Vlasov equation on Reissner-Nordström spacetimes, showing decay rates and non-decay phenomena.

Minkowski space is shown to be globally stable as a solution to the Einstein--Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the "wave zone", and then proving a small data semi-global existence result for the characteristic initial value p…

Proves existence and trapped surface formation for Einstein-Vlasov system without symmetry assumptions.

Future stability of FLRW solutions in expanding 3D space is shown for compact perturbations.

We prove that the maximal development of any spherically symmetric spacetime with collisionless matter (obeying the Vlasov equation) or a massless scalar field (obeying the massless wave equation) and possessing a constant mean curvature $S^1 \times S^2$ Cauchy surface also contains a maximal Cauchy surface. Combining …

It is shown that the initial singularities in spatially compact spacetimes with spherical, plane or hyperbolic symmetry admitting a compact constant mean curvature hypersurface are crushing singularities when the matter content of spacetime is described by the Vlasov equation (collisionless matter) or the wave equation…

The paper analyzes McKean-Vlasov equations with hitting times, proving global solvability.

In this thesis, we consider the suitability of using the charged cold fluid model in the description of ultra-relativistic beams. The method that we have used is the following. Firstly, the necessary notions of kinetic theory and differential geometry of second order differential equations are explained. Then an averag…

Massless Majorana spinors cannot exist in Kerr spacetime under certain conditions.

Existence of calibrated local stochastic volatility models proven for non-regular coefficients.

This paper extends transfer operator theory to McKean-Vlasov equations.

Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex $4\times 4$ symmetric matrices. It is shown that the unfolded equations of free massless fields, that have a form of multidimensional Schrodinger equations, naturally distinguish between positive- and negative-frequen…

We get decay rate of higher derivatives of nonlinear massless Dirac equations with a kind of "good" spin null form. The method we rely on is similar to that of Li and Zang. However, they only give the decay rate of solution itself to nonlinear massless Dirac system.

Unified geometric formulation of Maxwell-Vlasov system using presymplectic and symmetry reduction.

Novel RKHS approach solves complex financial model equations.

Neural network factorization speeds up Vlasov equation simulations.

We characterize stationary solutions to McKean-Vlasov equations on the circle.

Researchers resolve string theory ambiguities and define a new metric for massless spectrum.

We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test functions to be chosen in the weak formulation of the kinetic model. This involves t…

Massless scalar and vector fields are coupled to Lyra geometry by means of Duffin-Kemmer-Petiau (DKP) theory. Using Schwinger Variational Principle, equations of motion, conservation laws and gauge symmetry are implemented. We find that the scalar field couples to the anholonomic part of the torsion tensor, and the gau…

New model explains market dynamics with phase transitions and non-linear interactions.

New method improves Euler approximation for local stochastic volatility models.

We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are intro…

Improved latent dynamics identification framework reduces training time and improves accuracy.

A new method solves complex control problems with random coefficients.

Researchers study spectral asymmetry using pseudodifferential projections on the massless Dirac operator.

We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution equation. Moreover, we show that in a wide range of cases the evolution of the cum…

Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describ…

The Teukolsky equations are currently the leading approach for analysing stability of linear massless fields propagating in rotating black holes. It has recently been shown that the geometry of these equations can be understood in terms of a connection constructed from the conformal and complex structure of Petrov type…

New method solves supercooled Stefan problem, proving minimal solutions are physical.

We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework is a special case of the so-called Cosserat theory of elasticity. Rotations of p…

Study constructs scattering theory for massless Dirac field on Kerr spacetime.

Proves local existence and extension principle for Einstein Yang--Mills system with spherical symmetry.

A Carter like constant for the geodesic motion in the $Y(p,q)$ Einstein-Sasaki geometries is presented. This constant is functionally independent with respect to the five known constants for the geometry. Since the geometry is five dimensional and the number of independent constants of motion is at least six, the geode…

Paper studies particle method for LSV model calibration, proving convergence and error bounds.

This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for some of these equations are established. Moreover, in the course of the article, …

The global symmetry algebras of partially-massless (PM) higher-spin (HS) fields in (A)dS$_{d+1}$ are studied. The algebras involving PM generators up to depth $2\,(\ell-1)$ are defined as the maximal symmetries of free conformal scalar field with $2\,\ell$ order wave equation in $d$ dimensions. We review the constructi…

Unified framework for implicit generative models with theoretical guarantees.

Analysis of Vlasov plasma dynamics using matched pair Lie-Poisson formulation.

Proposes methods to include distributional information in MV-SDEs for better modeling of interacting particle systems.

Study proves stability of big bang singularity in complex system.

The paper studies stochastic optimization on matrices and its limits as dimensions grow.

Study of Bondi-Sachs formalism for massless scalar field with zero cosmological constant.

Study phase transitions in noisy transformer dynamics on spheres.

Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality between Minkowski space-time and a Conformal Field Theory defined on the boundary of …

Letter analyzes training dynamics of a nonlinear contrastive learning model in high dimensions.

Proves existence and uniqueness of calibrated LSV model.

The action principle by Low [Proc. R. Soc. Lond. A 248, 282--287] for the classic Vlasov-Maxwell system contains a mix of Eulerian and Lagrangian variables. This renders the Noether analysis of reparametrization symmetries inconvenient, especially since the well-known energy- and momentum-conservation laws for the syst…