Related papers: The oscillating random walk on $\mathbb{Z}$

In a recent paper of Eichelsbacher and Koenig (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a k-dimensional random walk conditioned to stay in…

The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as L{\'e}vy walks for which the persistence times depend on some internal…

In this paper we consider a particular version of the random walk with restarts: random reset events which bring suddenly the system to the starting value. We analyze its relevant statistical properties like the transition probability and…

We give a simple proof for recurrence of vertex reinforced jump process on \(\mathbb{Z}^d\), under strong reinforcement. Moreover, we show how the previous result implies that linearly edge-reinforced random walk on \ \(\mathbb{Z}^d\) is…

Let $G$ be a connected graph of uniformly bounded degree. A $k$ non-backtracking random walk ($k$-NBRW) $(X_n)_{n =0}^{\infty}$ on $G$ evolves according to the following rule: Given $ (X_n)_{n =0}^{s}$, at time $s+1$ the walk picks at…

The present paper extends the earlier results obtained by Abramov [`Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes' \emph{Bull. Aust. Math. Soc.} \textbf{109} (2024), 393--402] for the case of…

First, we prove a \emph{local almost sure central limit theorem} for lattice random walks in the plane. The corresponding version for random walks in the line was considered by the author in \cite{5}. This gives us a quantitative version of…

In this note, we prove without using Fourier analysis that the symmetric square integrable random walks in $\Z^{2}$ are recurrent.

We study branching random walks in random i.i.d. environment in $\Z^d, d \geq 1$. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience,…

In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides…

We study a particular class of trace-preserving completely positive maps, called PQ-channels, for which classical and quantum evolutions are isolated in a certain sense. By combining open quantum random walks with a notion of recurrence, we…

We call one-way simple random walk a random walk in the quadrant Z_+^n whose increments belong to the canonical base. In relation with representation theory of Lie algebras and superalgebras, we describe the law of such a random walk…

Hypergraph has been selected as a powerful candidate for characterizing higher-order networks and has received increasing attention in recent years. In this article, we study random walks with resetting on hypergraph by utilizing spectral…

We investigate if the degradation of a quantum directional reference frame through repeated use can be modeled as a classical direction undergoing a random walk on a sphere. We demonstrate that the behaviour of the fidelity for a degrading…

We consider random walks on the group of orientation-preserving homeomorphisms of the real line ${\mathbb R}$. In particular, the fundamental question of uniqueness of an invariant measure of the generated process is raised. This problem…

Recurrence in the classical random walk is well known and described by the P\'olya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to return to its origin. Under…

We propose an implementation of a quantum walk on a circle on an optomechanical system by encoding the walker on the phase space of a radiation field and the coin on a two-level state of a mechanical resonator. The dynamics of the system is…

We consider random walks associated with conductances on Delaunay triangulations, Gabriel graphs and skeletons of Voronoi tilings which are generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on point processes and…

Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…

We prove that for a random walk on the real line whose increments have zero mean and are either integer-valued or spread out (i.e. the distributions of the steps of the walk are eventually non-singular), the Markov chain of overshoots above…