Related papers: Multidimensional random walk with reflections
We study $\mathbb Z$- and $\mathbb N$-extensions of interval maps with at most countably many full branches modelling one-dimensional random walks without and with a reflective boundary. We analyse the associated Gurevich pressure and…
Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the…
The reflected process of a random walk or L\'evy process arises in many areas of applied probability, and a question of particular interest is how the tail of the distribution of the heights of the excursions away from zero behaves…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
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…
We report on the asymptotic behaviour of a new model of random walk, we term the bindweed model, evolving in a random environment on an infinite multiplexed tree. The term \textit{multiplexed} means that the model can be viewed as a nearest…
We define a random walk problem which admits analytic results, on a class of infinite periodic lattices which are directed and colored. Our approach is motivated from the fact that such lattices arise in string theoretic constructs of…
We present here a system with collection of random walks relaying a signal in one dimension in the presence of delays. We are interested in the time for a signal to travel from one end (start) to the other end (finish) of the lined group of…
The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…
We consider random walks on $\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of…
In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce…
We study the winding behavior of random walks on two oriented square lattices. One common feature of these walks is that they are bound to revolve clockwise. We also obtain quantitative results of transience/recurrence for each walk.
The authors propose a new variation of random walks called ladder chains $L(r,s,p)$. We extend concepts such as ruin probability, hitting time, transience and recurrence of random walks to ladder chain. Take $L(2,2,p)$ for instance, we find…
In the randomly-oriented Manhattan lattice, every line in $\mathbb{Z}^d$ is assigned a uniform random direction. We consider the directed graph whose vertex set is $\mathbb{Z}^d$ and whose edges connect nearest neighbours, but only in the…
We study a generalisation of the one-dimensional Rademacher random walk introduced in Bhattacharya and Volkov (2023) to $\mathbb{Z}^2$ (for $d\ge 3$, the Rademacher random walk is always transient, as follows from Theorem 8.8 in Englander…
We consider the dynamics of lattice random walks with resetting. The walker moving randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a constant probability $r$. We construct a discrete renewal…
We define a random walk of a particle in $\mathbb{R}^3$ where the space is rotating. The particle is not glued to the space and will collide with it at random times, resulting in changes in its velocity and direction. After many collisions,…
In recent years, computer simulations are playing a fundamental role in unveiling some of the most intriguing features of prime numbers. In this work, we define an algorithm for a deterministic walk through a two-dimensional grid that we…
A random walk with echoed steps (RWES) is a process $\{\tilde{S}_n\}_{n\geq1}=\{\tilde{X}_1+\cdots+\tilde{X}_n\}_{n\geq1}$ that inserts memory and echo into an ordinary random walk (ORW) with i.i.d. steps, $X_1+\cdots+X_n$. The RWES is…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…