相关论文: Diagrammar For Random Flight Motion

In the spirit of the macroscopic crowd motion models with hard congestion (i.e. a strong density constraint $\rho\leq 1$) introduced by Maury {\it et al.} some years ago, we analyze a variant of the same models where diffusion of the agents…

A method to efficiently compute, in a automatic way, helicity amplitudes for arbitrary scattering processes at leading order in the Standard Model is presented. The scattering amplitude is evaluated recursively through a set of…

We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…

We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the…

We have discovered analytical expressions for the probability density function (PDF) of photons that are multiply scattered in relativistic flows, under the assumption of isotropic and inelastic scattering. These expressions characterize…

Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…

We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weakly non-linear approximations to problems whose linearized…

Diffusion-based posterior samplers use pretrained diffusion priors to sample from measurement- or reward-conditioned posteriors, and are widely used for inverse problems. Yet their theoretical behavior remains poorly understood: even with…

In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was…

We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the refractive index properties, but they are not differentiable. We…

Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…

We consider a particular class of n-dimensional homogeneous diffusions all of which have an identity diffusion matrix and a drift function that is piecewise constant and scale invariant. Abstract stochastic calculus immediately gives us…

We extend the random walk framework to include compounded steps, providing first-passage time (FPT) properties for a new class of superdiffusive processes, which are governed by the space-fractional spectral Fokker-Planck equation. This…

We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…

We develop a formalism for particle production in a field theory coupled to a strong time-dependent external source. An example of such a theory is the Color Glass Condensate. We derive a formula, in terms of cut vacuum-vacuum Feynman…

This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I start from a rigorous treatment of a…

Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…

We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…

Using a probabilistic neural network and Lagrangian observations from the Global Drifter Program, we model the single particle transition probability density function (pdf) of ocean surface drifters. The transition pdf is represented by a…

Functionals of Brownian/non-Brownian motions have diverse applications and attracted a lot of interest of scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of…