Related papers: Anomalous Roughness, Localization, and Globally Co…
We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…
In previous work by Avena and den Hollander, a model of a one-dimensional random walk in a dynamic random environment was proposed where the random environment is resampled from a given law along a growing sequence of deterministic times.…
We describe scaling limits of recurrent excited random walks (ERWs) on integers in i.i.d. cookie environments with a bounded number of cookies per site. We allow both positive and negative excitations. It is known that ERW is recurrent if…
In the frequency domain, the nearly constant loss, is characterized by a slope 1 in log of the real part of the electrical conductivity vs log frequency plots. It can be explained by an anomalous diffusion, defined by a random walk with the…
A one-dimensional system of nonintersecting Brownian particles is constructed as the diffusion scaling limit of Fisher's vicious random walk model. $N$ Brownian particles start from the origin at time $t=0$ and undergo mutually avoiding…
An excited random walk is a non-Markovian extension of the simple random walk, in which the walk's behavior at time $n$ is impacted by the path it has taken up to time $n$. The properties of an excited random walk are more difficult to…
We study the asymptotic behaviour of random walks in i.i.d. random environments on $\Z^d$. The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when…
We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability $r$, and with…
We study continuous-time (variable speed) random walks in random environments on $\mathbb{Z}^d$, $d\ge2$, where, at time $t$, the walk at $x$ jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary…
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…
We consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites. The configuration comprising the graph, the starting point of the walk, and the locations of the trap sites is taken to be exactly…
We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in…
Quantum walks are promising for information processing tasks because on regular graphs they spread quadratically faster than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson…
We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the…
The edge-reinforced random walk (ERRW) is a random process on the vertices of a graph that is more likely to cross the edges it has visited in the past. Depending on the strength of the reinforcement, the ERRW of a single particle can…
This paper considers 1-dimensional generalized random walks in random scenery. That is, the steps of the walk are generated by an arbitrary stationary process, and also the scenery is a priori arbitrary stationary. Under an ergodicity…
We derive an anomalous, sub-diffusive scaling limit for a one-dimensional version of the Mott random walk. The limiting process can be viewed heuristically as a one-dimensional diffusion with an absolutely continuous speed measure and a…
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…
Passive random walker dynamics is introduced on a growing surface. The walker is designed to drift upward or downward and then follow specific topological features, such as hill tops or valley bottoms, of the fluctuating surface. The…
We consider one-dimensional activated random walk (ARW) on $\mathbb{Z}$ started from a `point source' initial condition, with many particles at the origin and no other particles. We prove that, uniformly throughout a macroscopic window…