Related papers: On the asymptotics of the scenery flow
We show that every diffeomorphism with mostly contracting center direction exhibits a geometric-combinatorial structure, which we call \emph{skeleton}, that determines the number, basins and supports of the physical measures. Furthermore,…
In this paper we study the behavior of an incompressible viscous fluid moving between two very close surfaces also in motion. Using the asymptotic expansion method we formally justify two models, a lubrication model and a shallow water…
The paper compares probabilistic and exact methods for estimating the asymptotic behavior of summation arithmetic functions, and estimates of the results are obtained by precise methods. Conditions for stationarity in the broad sense are…
Some asymptotic properties of a Brownian motion in multifractal time, also called multifractal random walk, are established. We show the almost sure and $L^1$ convergence of its structure function. This is an issue directly connected to the…
Center foliations of partially hyperbolic diffeomorphisms may exhibit pathological behavior from a measure-theoretical viewpoint: quite often, the disintegration of the ambient volume measure along the center leaves consists of atomic…
Using experimental longitudinal and transverse velocities data for very high Reynolds number turbulence, we study both anisotropy and asymmetry of turbulence. These both seem to be related to small scale turbulent structures, and to…
Strongly consistent estimates are shown, via relative frequency, for the probability of "white balls" inside a dichotomous urn when such a probability is an arbitrary continuous time dependent function over a bounded time interval. The…
By developing the entropy theory of random walks on equivalence relations and analyzing the asymptotic geometry of horospheric products we describe the Poisson boundary for random walks on random horospheric products of trees.
Parallel shear flows come with continuous symmetries of translation in the downstream and spanwise direction. As a consequence, flow states that differ in their spanwise or downstream location but are otherwise identical are dynamically…
Fast advection asymptotics for a stochastic reaction-diffusion-advection equation are studied in this paper. To describe the asymptotics, one should consider a suitable class of SPDEs defined on a graph, corresponding to the stream function…
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…
In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B…
This article is on collective phenomena in pedestrian dynamics during the assembling and dispersal phases of gatherings. To date pedestrian dynamics have been primarily studied in the natural and engineering sciences. Pedestrians are…
A Bernoulli random walk is a random trajectory starting from 0 and having i.i.d. increments, each of them being $+1$ or -1, equally likely. The other families cited in the title are Bernoulli random walks under various conditionings. A peak…
The transport of slightly deformable chiral objects in a uniform shear flow is investigated. Depending on the equilibrium configuration one finds up to four different asymptotic states that can be distinguished by a lateral drift velocity…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
The randomization effect of the two-way (particle-flow) interaction has been studied and quantified using the notion of distributed chaos and the results of numerical simulations and laboratory measurements. It is shown, in particular, that…
We propose an analytical method to determine the shape of density profiles in the asymptotic long time limit for a broad class of coupled continuous time random walks which operate in the ballistic regime. In particular, we show that…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…