Related papers: Harmonic functions for singular quadrant walks

We construct the conditional version of $k$ independent and identically distributed random walks on $\R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random…

For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the…

In analyzing a simple random walk on the Heisenberg group we encounter the problem of bounding the extreme eigenvalues of an $n\times n$ matrix of the form $M=C+D$ where $C$ is a circulant and $D$ a diagonal matrix. The discrete…

We provide a random walk in random scenery representation of a new class of stable self-similar processes with stationary increments introduced recently by Jung, Owada and Samorodnitsky. In the functional limit theorem they provided, only a…

We consider one-dependent random walks on $\mathbb{Z}^d$ in random hypergeometric environment for $d\ge 3$. These are memory-one walks in a large class of environments parameterized by positive weights on directed edges and on pairs of…

We survey some geometrical properties of trajectories of $d$-dimensional random walks via the application of functional limit theorems. We focus on the functional law of large numbers and functional central limit theorem (Donsker's…

Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…

We consider a class of self-interacting random walks in deterministic or random environments, known as excited random walks or cookie walks, on the d-dimensional integer lattice. The main purpose of this paper is two-fold: to give a survey…

We prove a strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter $\gamma$. First, we establish that if…

We prove sharp asymptotic estimates for the rate of escape of the two-dimensional simple random walk conditioned to avoid a fixed finite set. We derive it from asymptotics available for the continuous analogue of this process (cf…

Random walks with a general, nonlinear barrier have found recent applications ranging from reionization topology to refinements in the excursion set theory of halos. Here, we derive the first-crossing distribution of random walks with a…

In this paper we consider a time-continuous random walk in $\mathbb{Z}^d$ in a dynamical random environment with symmetric jump rates to nearest neighbours. We assume that these random conductances are stationary and ergodic and, moreover,…

We consider a random walk on Z^d in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from x to nearest neighbor x+e is the same as to nearest neighbor x-e. Assuming that the environment is…

We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…

We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on $\Z^d$, $d\geq 3$, when the…

We introduce a technique to obtain pointwise upper and lower bounds for the Green's function of elliptic operators whose principal part is the Laplacian and that include a drift term diverging near the boundary like a power of the inverse…

We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…

The Dirac equation can be modelled as a quantum walk, with the quantum walk being: discrete in time and space (i.e. a unitary evolution of the wave-function of a particle on a lattice); homogeneous (i.e. translation-invariant and…

We study an homogeneous irreducible markovian random walk in a square lattice of arbitrary dimension, with an antisymmetric perturbation acting only in one point. We compute exactly spatial correction to the diffusive behaviour in the…

A simple symmetric random walk in the space $\mathbb{Z}^2$ is considered. The asymptotic behavior as the number of jumps tends to infinity of the probability that a fixed edge of the random walk lies in the polygon that forms the boundary…