Related papers: High Dimensional Random Walks Can Appear Low Dimen…
Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
We analyze the properties of a two and three dimensional quantum walk that are inspired by the idea of a brane-world model put forward by Rubakov and Shaposhnikov [1]. In that model, particles are dynamically confined on the brane due to…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding…
Dynamic systems characterized by diversified evolutions are not only more flexible, but also more resilient to attacks, failures and changing conditions. This article addresses the quantification of the diversity of non-linear transient…
Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity…
We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in Angel and Ray [3]. We show that almost surely the walker escapes the boundary of the map in positive speed and that the return probability to…
In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
Divergence in antigen response of the immune network is discussed, based on shape-space modelling. The present model extends the shape-space model by introducing the evolution of specificity of idiotypes. When the amount of external antigen…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
We construct a two-dimensional counterexample of a random walk in random environment (RWRE). The environment is stationary, mixing and perturbative, and the corresponding RWRE has non-trivial probability to wander off to the upper right.…
We introduce and discuss a minimal individual-based model for influenza dynamics. The model takes into account the effects of specific immunization against viral strains, but also infectivity randomness and the presence of a short-lived…
We consider a one-dimensional simple symmetric exclusion process in equilibrium, constituting a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We…
Starting from a simple animal-biology example, a general, somewhat counter-intuitive property of diffusion random walks is presented. It is shown that for any (non-homogeneous) purely diffusing system, under any isotropic uniform incidence,…
We propose that the effective dimensionality of the space we live in depends on the length scale we are probing. As the length scale increases, new dimensions open up. At short scales the space is lower dimensional; at the intermediate…
We introduce a family of two-dimensional reflected random walks in the positive quadrant and study their Martin boundary. While the minimal boundary is systematically equal to a union of two points, the full Martin boundary exhibits an…