Related papers: A pathwise approach to relativistic diffusions
A criterion for proving a strong form of propagation of chaos on the path space, known as entropy chaos, for a general interacting diffusion system is proposed. Our analysis focuses on the class of conservative diffusions introduced by…
We present the idea of intertwining of two diffusions by Feynman-Kac operators. We present some variations and implications of the method and give examples of its applications. Among others, it turns out to be a very useful tool for finding…
In this paper, we study univariate and planar random motions with variable propagation speeds. We first consider motions with space-varying velocity, which can be reduced to constant-velocity motions by means of suitable nonlinear…
A heuristic approach for collisionless perpendicular diffusion of energetic particles is presented. Analytic forms for the corresponding diffusion coefficient are derived. The heuristic approach presented here explains the parameter $a^2$…
Random walks of particles on a lattice are a classical paradigm for the microscopic mechanism underlying diffusive processes. In deterministic walks, the role of space and time can be reversed, and the microscopic dynamics can produce quite…
The particle diffusion in a fluid is a classical topic that dates back to more than one century ago. However, a full solution to this issue still lacks. In this work the velocity autocorrelation function and the diffusion constant are…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions can be written as a euclideen Schr\"odinger equation in which the wave function is the probability distribution and the Hamiltonian is…
A canonical structure compatible with the action of the Lorentz group can be obtained considering the energy and time as conjugate variables of an extended phase space. Scalar probability waves, describing free relativistic particles, are…
The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward…
A vacuum medium model is advanced. The motion of a relativistic particle in relation to its interaction with the medium is discussed. It is predicted that elementary excitations of the vacuum, called "inertons," should exist. The equations…
A rigorous definition of a path integral for a spinning particle in three dimensions is given on a regular cubic lattice. The critical diffusion constant and the associated critical exponents in each spin are calculated. Continuum field…
We consider the diffusion of markers in a layered medium, with the lateral diffusion coefficient being the function of hight. We show that the probability density of the lateral displacements follows one-dimensional Batchelor's equation…
We consider a class of time-homogeneous diffusion processes on $\mathbb{R}^{n}$ with common invariant measure but varying volatility matrices. In Euclidean space, we show via stochastic control of the diffusion coefficient that the…
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…
We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations. All these models have classical unique solutions, at…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
Levy walks define a fundamental concept in random walk theory which allows one to model diffusive spreading that is faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a…
Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…
A consistent theory, which describes the incoherent scattering of classically moving relativistic particles by the nuclei of crystal planes without any phenomenological parameter is presented. The basic notions of quantum mechanics are…
The variational principle for the special and general relativistic hydrodynamics are discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable…