Related papers: Density Profiles in Open Superdiffusive Systems
We study the elephant random walk in arbitrary dimension $d\geq 1$. Our main focus is the limiting random variable appearing in the superdiffusive regime. Building on a link between the elephant random walk and P\'olya-type urn models, we…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
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…
This paper investigates the score-based diffusion models for density estimation when the target density admits a factorizable low-dimensional nonparametric structure. To be specific, we show that when the log density admits a $d^*$-way…
We introduce a discrete-time random walk model on a one-dimensional lattice with a nonconstant sojourn time and prove that the discrete density converges to a solution of a continuum diffusion equation. Our random walk model is not…
Tracer diffusion in single-file systems, where particles are restricted to move on a line without passing each other, has been a fertile ground to investigate anomalous diffusion and strong memory effects. While the long-time behavior of…
Strong anomalous diffusion phenomena are often observed in complex physical and biological systems, which are characterized by the nonlinear spectrum of exponents $q\nu(q)$ by measuring the absolute $q$-th moment $\langle |x|^q\rangle$.…
We study the barrier crossing of a particle driven by white symmetric Levy noise of index $\alpha$ and intensity $DD for three different generic types of potentials: (a) a bistable potential; (b) a metastable potential; and (c) a truncated…
Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of L\'evy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times…
We consider an open one dimensional lattice gas on sites $i=1,...,N$, with particles jumping independently with rate 1 to neighboring interior empty sites, the {\it simple symmetric exclusion process}. The particle fluxes at the left and…
The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination…
A L{\'e}vy walk of order $\beta$ is studied on an interval of length $L$, driven out of equilibrium by different-density boundary baths. The anomalous current generated under these settings is nonlocally related to the density profile…
In this paper, we modify the Langevin dynamics associated to the generalized Curie-Weiss model by introducing noisy and dissipative evolution in the interaction potential. We show that, when a zero-mean Gaussian is taken as single-site…
We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
The L\'evy walk is a non-Brownian random walk model that has been found to describe anomalous dynamic phenomena in diverse fields ranging from biology over quantum physics to ecology. Recurrently occurring problems are to examine whether…
A version of the saddle point method is developed, which allows one to describe exactly the asymptotic behavior of distribution densities of Levy driven stochastic integrals with deterministic kernels. Exact asymptotic behavior is…
We consider a one-dimensional chain of coupled oscillators in contact at both ends with heat baths at different temperatures, and subject to an external force at one end. The Hamiltonian dynamics in the bulk is perturbed by random exchanges…
Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…