Related papers: Limit laws for discrete excursions and meanders an…
In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study…
In this paper we consider the one-dimensional quantum random walk X^{varphi} _n at time n starting from initial qubit state varphi determined by 2 times 2 unitary matrix U. We give a combinatorial expression for the characteristic function…
This survey is a collection of various results and formulas by different authors on the areas (integrals) of five related processes, viz.\spacefactor =1000 Brownian motion, bridge, excursion, meander and double meander; for the Brownian…
For the perimeter length and the area of the convex hull of the first $n$ steps of a planar random walk, we study $n \to \infty$ mean and variance asymptotics and establish non-Gaussian distributional limits. Our results apply to random…
In this article, we study the extremal processes of branching Brownian motions conditioned on having an unusually large maximum. The limiting point measures form a one-parameter family and are the decoration point measures in the extremal…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method…
We give an explicit construction of the scaling limit of the minimum spanning tree of the complete graph. The limit object is described using a recursive construction involving the convex minorants of a Brownian motion with parabolic drift…
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…
We apply results from Baryshnikov, Brady, Bressler and Pemantle (2008) to compute limiting probability profiles for various quantum random walks in one and two dimensions. Using analytic machinery we show some features of the limit…
In this paper we present a new and flexible method to show that, in one dimension, various self-repellent random walks converge to self-repellent Brownian motion in the limit of weak interaction after appropriate space-time scaling. Our…
This paper introduces nondeterministic walks, a new variant of one-dimensional discrete walks. The main difference to classical walks is that its nondeterministic steps consist of sets of steps from a predefined set such that all possible…
In arXiv:1609.05666v1 [math.PR] a functional limit theorem was proved. It states that symmetric processes associated with resistance metric measure spaces converge when the underlying spaces converge with respect to the…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
We consider local singular perturbations of a one-dimensional Laplace operator from the point of view of semigroup theory. Under certain assumptions, we prove the convergence of the corresponding semigroups to the heat semigroup with…
A matrix random walk is a stochastic process of the form $B_k = (I+A_1)\cdots(I+A_k)$ where $A_j$ are independent ``step'' matrices in $\mathrm{M}_N(\mathbb{C})$. With the right entry-covariance, a rescaled matrix random walk converges to…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous…
We consider the limit behavior of a one-dimensional random walk with unit jumps whose transition probabilities are modified every time the walk hits zero. The invariance principle is proved in the scheme of series where the size of…
We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\"{u}tz-type formula is derived for the transition probability. We investigate an…