Related papers: A problem in one-dimensional diffusion-limited agg…
For real world systems, nonuniform medium is ubiquitous. Therefore, we investigate the diffusion-limited-aggregation process on a two dimensional directed small-world network instead of regular lattice. The network structure is established…
Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly…
We investigate the run and tumble particle (RTP), also known as persistent Brownian motion, in one dimension. A telegraphic noise $\sigma(t)$ drives the particle which changes between $\pm 1$ values with some rates. Denoting the rate of…
We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate $r$. We compute the non-equilibrium stationary state…
The method of iterated conformal maps for the study of Diffusion Limited Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and related processes. We emphasize the fundamental difference between these processes: DLA…
This work studies the recursive robust principal components analysis (PCA) problem. If the outlier is the signal-of-interest, this problem can be interpreted as one of recursively recovering a time sequence of sparse vectors, $S_t$, in the…
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
We study a gas of $N$ Brownian particles in the presence of a common stochastic diffusivity $D(t)=B^2(t)$, where $B(t)$ represents a one-dimensional Brownian motion at time $t$. Starting from all the particles localized at the origin, the…
In recent years, several experiments highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows…
Sampling a random permutation with restricted positions, or equivalently approximating the permanent of a 0-1 matrix, is a fundamental problem in computer science, with several notable results achieved over the years. However, existing…
Consider the random set composed of particles initially distributed on Zd, d >= 2, according to a Poisson point process of intensity u > 0 and moving as independent simple symmetric random walks, the trap particles. We are interested in the…
We investigate the maximal size of an increasing subset among points randomly sampled from certain probability densities. Kerov and Vershik's celebrated result states that the largest increasing subset among $N$ uniformly random points on…
We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over…
In this paper, we analyze the scaling behavior of \emph{Diffusion Limited Aggregation} (DLA) simulated by Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns in a good…
We present extensive molecular dynamics simulations of the motion of a single linear rigid molecule in a two-dimensional random array of fixed obstacles. The diffusion constant for the center of mass translation, $D_{\rm CM}$, and for…
We discuss contemporaneous aggregation of independent copies of a triangular array of random-coefficient AR(1) processes with i.i.d. innovations belonging to the domain of attraction of an infinitely divisible law W. The limiting aggregated…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
Boundary value problems for diffusion in singularly perturbed domains (domains with small holes removed from the interior) is a topic of considerable current interest. Applications include intracellular diffusive transport and the spread of…