Related papers: Heavy-tailed targets and (ab)normal asymptotics in…
Probability density functions (pdfs) of $^{13}CO$ emission line centroid (line-of-sight, intensity-weighted average) velocities are presented for several densely sampled molecular clouds as quantitative descriptors of their underlying…
We study a two-dimensional diffusive motion of a tracer particle in restricted, crowded anisotropic geometries. The underlying medium is the same as in our previous work [J. Chem. Phys. 140, 044706 (2014)] in which standard, gaussian…
We investigate the Cauchy problem and the diffusion asymptotics for a spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck operator. We derive the global well-posedness result with instantaneous smoothness effect,…
The dynamics of the open or closed state region of an ion channel may be described by a probability density $p(x,t)$ which satisfies a Fokker-Planck equation. The closed state dwell-time distribution $f_c(t)$ derived from the Fokker-Planck…
We consider super-diffusive L\'evy walks in $d \geqslant 2$ dimensions when the duration of a single step, i.e., a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean.…
Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such…
We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as…
In this article, we perform an asymptotic analysis of a nonlocal reaction-diffusion equation, with a fractional laplacian as the diffusion term and with a nonlocal reaction term. Such equation models the evolutionary dynamics of a…
We study a lattice model describing the non-equilibrium dynamics emerging from the pulling of a tracer particle through a disordered medium occupied by randomly placed obstacles. The model is considered in a restricted geometry pertinent…
In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are…
In this paper, we study a stochastically driven non-equilibrium quantum system where the driving protocols consist of hopping and waiting processes. The waiting times between two hopping processes satisfy a heavy-tailed distribution. By…
We study large deviations for the time average of the Ornstein-Uhlenbeck process raised to an arbitrary power. We prove that beyond a critical value, large deviations are subexponential in time, with a non-convex rate function whose main…
Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing…
The L\'evy-Lorentz gas describes the motion of a particle on the real line in the presence of a random array of scattering points, whose distances between neighboring points are heavy-tailed i.i.d. random variables with finite mean. The…
The silo discharge process is studied by molecular dynamics simulations. The development of the velocity profile and the probability density function for the displacements in the horizontal and vertical axis are obtained. The PDFs obtained…
A generalized Fokker-Planck equation is derived to describe particle kinetics in specific situations when the probability transition function (PTF) has a long tail in momentum space. The equation is valid for an arbitrary value of the…
Subcritical transition of an inhomogeneous plasma where turbulences with different characteristic space-time scales coexist is analyzed with methods of statistical physics of turbulences. We derived the development equations of the…
Score-based diffusion models have become a powerful framework for generative modeling, with score estimation as a central statistical bottleneck. Existing guarantees for score estimation largely focus on light-tailed targets or rely on…
This article shows a strong averaging principle for diffusions driven by discontinuous heavy-tailed L\'evy noise, which are invariant on the compact horizontal leaves of a foliated manifold subject to small transversal random perturbations.…
Recently a new type of Kramers-Fokker-Planck Equation has been proposed [R. Friedrich et al. Phys. Rev. Lett. {\bf 96}, 230601 (2006)] describing anomalous diffusion in external potentials. In the present paper the explicit cases of a…