Related papers: On the asymptotics of the scenery flow

We detect, by using symplectic topology, invariant measures with large rotation vectors for a class of Hamiltonian flows.

For simulation models of pedestrian dynamics there are always the issues of calibration and validation. These are usually done by comparing measured properties of the dynamics found in observation, experiments and simulation in certain…

A numerical study of laminar flow through symmetric and slightly asymmetric sudden expansion, of expansion ratio 1:3, in channels with increasing cross section, is carried out using two different approaches - Conventional CFD and Lattice…

Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta.…

In this paper, following earlier results in [2] we derive the asymptotic distribution as $t \to \infty$, of the excursion of Brownian motion straddling $t$, into an interval $(a,b)$, conditional on the event that there is such an excursion.

The random flights are (continuous time) random walkswith finite velocity. Often, these models describe the stochastic motions arising in biology. In this paper we study the large time asymptotic behavior of random flights. We prove the…

For a symmetric random walk in $Z^2$ which does not necessarily have bounded jumps we study those points which are visited an unusually large number of times. We prove the analogue of the Erd\H{o}s-Taylor conjecture and obtain the…

We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…

Enstrophy is an averaged measure of fluid vorticity. This quantity is particularly important in {\em rotating} geophysical flows. We investigate the dynamical evolution of enstrophy for large-scale quasi-geostrophic flows under random wind…

We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [arXiv:1408.0628]. The system is a natural generalization of the coalescing Brownian motions. The main difference is that…

We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any…

This article considers execution and analysis of laboratory experiments of pedestrians moving in a quasi-one-dimensional system with periodic boundary conditions. To analyze characteristics of jams in the system we aim to use the whole…

Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…

It has become widely known that when two flows of pedestrians cross stripes emerge spontaneously by which the pedestrians of the two walking directions manage to pass each other in an orderly manner. In this work, we report about the…

We numerically study jamming transitions in pedestrian flow interacting with an attraction, mostly based on the social force model for pedestrians who can join the attraction. We formulate the joining probability as a function of social…

Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and…

The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just…

We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently:…

We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent…

Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper, we apply mathematically rigorous methods to showing why…