Related papers: A double large deviation principle for monge-amper…
We report a gravitational $BF$-type action principle propagating two (complex) degrees of freedom that, besides the gauge connection and the $B$ field, only employs an additional Lagrange multiplier. The action depends on two parameters and…
We establish a large-deviations principle for the largest eigenvalue of a generalized sample covariance matrix, meaning a matrix proportional to $Z^T \Gamma Z$, where $Z$ has i.i.d. real or complex entries and $\Gamma$ is not necessarily…
The dynamics of "dipolar particles", i.e. particles endowed with a four-vector mass dipole moment, is investigated using an action principle in general relativity. The action is a specific functional of the particle's world line, and of the…
Multigravity theories are constructed from the discretization of the extra dimension of five dimensional gravity. Using an ADM decomposition, the discretization is performed while maintaining the four dimensional diffeomorphism invariance…
We prove the small-noise large deviation principle for the three-dimensional primitive equations with transport noise and turbulent pressure. Transport noise is important for geophysical fluid dynamics applications, as it takes into account…
We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced…
Modified Newtonian Dynamics (MOND) provides a successful description of stellar and galactic dynamics on almost all astronomical scales. A key feature of MOND is the transition function from Newtonian to modified dynamics which corresponds…
The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.
For a fractional Brownian motion $B^H$ with Hurst parameter $H\in]{1/4},{1/2}[\cup]{1/2},1[$, multiple indefinite integrals on a simplex are constructed and the regularity of their sample paths are studied. Then, it is proved that the…
We introduce an integral representation of the Monge-Amp\`ere equation, which leads to a new finite difference method based upon numerical quadrature. The resulting scheme is monotone and fits immediately into existing convergence proofs…
Galactic systems, and the Universe at large, exhibit large dynamical anomalies: The observed matter in them falls very short of providing enough gravity to account for their dynamics. The mainstream response to this conundrum is to invoke…
We propose an extension to our monotone and convergent method for the Monge-Amp\`{e}re equation in dimension $d \geq2$, that incorporates the idea of filtered schemes. The method combines our original monotone operator with a more accurate…
We investigate particle laws of motion derived from nonstandard kinetic actions of a special form. We are guided by a phenomenological scheme--the modified dynamics (MOND)--that imputes the mass discrepancy observed in galactic systems to a…
In a recent paper by Ambr\'osio et al. [arXiv:2405.14799], it was shown that the gravitational force law of the Modified Newtonian Dynamics (MOND) phenomenology can be derived within the framework of entropic gravity and the holographic…
We study the validity of a large deviation principle for a class of stochastic nonlinear damped wave equations, of Klein-Gordon type, in the joint small mass and small noise limit. The friction term is assumed to be state dependent.
We consider the numerical solution of the optimal transport problem between densities that are supported on sets of unequal dimension. Recent work by McCann and Pass reformulates this problem into a non-local Monge-Amp\`ere type equation.…
We prove the the large deviation principle(LDP) for the law of the one-dimensional semilinear stochastic partial differential equations driven by nonlinear multiplicative noise. Firstly, combining the energy estimate and approximation…
A model for the static weak-field macroscopic medium is analyzed and the equation for the macroscopic gravitational potential is derived. This is a biharmonic equation which is a non-trivial generalization of the Poisson equation of…
One obtains a Maxwell-like structure of gravitation by applying the weak-field approximation to the well accepted theory of general relativity or by extending Newton's laws to time-dependent systems. This splits gravity in two parts, namely…
In this paper, we prove second derivative estimates together with classical solvability for the Dirichlet problem of certain Monge-Ampere type equations under sharp hypotheses. In particular we assume that the matrix function in the…