Related papers: On the connection between the Nekhoroshev theorem …
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…
The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…
We prove an upper bound for the number of Ruelle resonances for Koopman operators associated to real-analytic Anosov diffeomorphisms: in dimension $d$, the number of resonances larger than $r$ is a $\mathcal{O}(|\log r|^d)$ when $r$ goes to…
We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…
What is the optimal way to approximate a high-dimensional diffusion process by one in which the coordinates are independent? This paper presents a construction, called the \emph{independent projection}, which is optimal for two natural…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
We prove the existence of diffusing solutions in the motion of a charged particle in the presence of an ABC magnetic field. The equations of motion are modeled by a 3DOF Hamiltonian system depending on two parameters. For small values of…
The Arnold diffusion constitutes a dynamical phenomenon which may occur in the phase space of a non-integrable Hamiltonian system whenever the number of the system degrees of freedom is $M \geq 3$. The diffusion is mediated by a web-like…
A simple model of random Brownian walk of a spherical mesoscopic particle in viscous liquids is proposed. The model can be both solved analytically and simulated numerically. The analytic solution gives the known Eistein-Smoluchowski…
We study some estimators of the Hurst index and the diffusion coefficient of the fractional Gompertz diffusion process and prove that they are strongly consistent and most of them are asymptotically normal. Moreover, we compare the…
The diffusion coefficient--a measure of dissipation, and the entropy--a measure of fluctuation are found to be intimately correlated in many physical systems. Unlike the fluctuation dissipation theorem in linear response theory, the…
Model of laminated wave turbulence allows to study statistical and discrete layers of turbulence in the frame of the same model. Statistical layer is described by Zakharov-Kolmogorov energy spectra in the case of irrational enough…
In circular particle accelerators, storage rings, or colliders, mitigating beam losses is critical to ensuring optimal performance, particularly for rings that include superconducting magnets. A thorough understanding of beam-halo dynamics…
Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different…
We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter $\theta_1$ in a non-degenerate diffusion coefficient and a parameter…
Given a probability distribution in R^n with general (non-white) covariance, a classical estimator of the covariance matrix is the sample covariance matrix obtained from a sample of N independent points. What is the optimal sample size N =…
The pitch-angle diffusion coefficient quantifies the effect of pitch-angle scattering on charged particles propagating through turbulent magnetic fields and is a key ingredient in understanding the diffusion of these particles along the…