Related papers: Comment on "Non-Normalizable Densities in Strong A…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
Given a sequence of lattice approximations $D_N\subset\mathbb Z^2$ of a bounded continuum domain $D\subset\mathbb R^2$ with the vertices outside $D_N$ fused together into one boundary vertex $\varrho$, we consider discrete-time simple…
The emergence of particle irreversibility in periodically driven colloidal suspensions has been interpreted as resulting either from a nonequilibrium phase transition to an absorbing state or from the chaotic nature of particle…
In this note, we establish that the stationary distribution of a possibly non-equilibrium Langevin diffusion converges, as the damping parameter goes to infinity (or equivalently in the Smoluchowski-Kramers vanishing mass limit), toward a…
Classes of multivariate and cone valued infinitely divisible Gamma distributions are introduced. Particular emphasis is put on the cone-valued case, due to the relevance of infinitely divisible distributions on the positive semi-definite…
In this paper, we establish a general convergence theorem for solutions of multivariate stochastic differential equations with countably many singular terms expressed as integrals with respect to local times. The processes under…
In this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this…
We show that the empirical spectral distribution (ESD) of the sample autocovariance matrix (ACVM) converges as the dimension increases, when the time series is a linear process with reasonable restriction on the coefficients. The limit does…
In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on unit cell of constant length) whose heights…
Relativistic and non-relativistic fluid equations can exhibit finite time singular solutions including density singularities appearing in collapse or compression systems and gradient singularities in shock waves. However, only the…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
This paper studies particle propagation in a one-dimensional inhomogeneous medium where the laws of motion are generated by chaotic and deterministic local maps. Assuming that the particle's initial location is random and uniformly…
We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…
Diffusion occurs in numerous physical systems throughout nature, drawing its generality from the universality of the central limit theorem. Around a century ago it was realized that an extension to this type of dynamics can be obtained in…
We report measurements of intensity distributions of transmitted microwave radiation in quasi-1D samples with lengths L as large as the localization length $\xi$. In contrast to negative exponential statistics found in the diffusive limit,…
According to the Dudley-Wichura extension of the Skorohod representation theorem, convergence in distribution to a limit in a separable set is equivalent to the existence of a coupling with elements converging a.s. in the metric. A density…
We consider the distribution of a graph invariant of central similarity proximity catch digraphs (PCDs) based on one dimensional data. The central similarity PCDs are also a special type of parameterized random digraph family defined with…
Cosmological linear perturbation theory predicts that the peculiar velocity $V(x)$ and the matter overdensity $\delta(x)$ at a same point $x$ are statistically independent quantities, as log as the initial density fluctuations are random…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…
We consider $N$ two-dimensional Ising models coupled in presence of quenched disorder and use scale invariant scattering theory to exactly show the presence of a line of renormalization group fixed points for any fixed value of $N$ other…