Related papers: The greedy walk on an inhomogeneous Poisson proces…
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…
The investigation of random walks is central to a variety of stochastic processes in physics, chemistry, and biology. To describe a transport phenomenon, we study a variant of the one-dimensional persistent random walk, which we call a…
As a strategy to complete games quickly, we investigate one-dimensional random walks where the step length increases deterministically upon each return to the origin. When the step length after the kth return equals k, the displacement of…
The L\'evy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, L\'evy walks with power…
We study the asymptotic behavior of ``true" self-avoiding random walks on general infinite locally finite trees. In this model, the walk starts at the root and, at each step, from its current vertex chooses a neighboring edge to traverse…
We study adaptation of a haploid asexual population on a fitness landscape defined over binary genotype sequences of length $L$. We consider greedy adaptive walks in which the population moves to the fittest among all single mutant…
We study an iterative selection problem over N i.i.d. discrete-time stochastic processes with independent increments. At each stage, a fixed number of processes are retained based on their observed values. Under this simple model, we prove…
Motivated by a problem arising from pharmaceutical science [B. Baeumer et al., Discr. Contin. Dyn. Sys. B 12], we study random walks on the contact graph of a bidisperse random sphere packing. For a random walk on the unweighted graph that…
The main purpose of this thesis is to study the interplay between geometric properties of infinite graphs and analytic and probabilistic objects such as transition operators, harmonic functions and random walks on these graphs. For a…
Excited random walk is a process that has a drift to the right whenever it encounters a new vertex. The paper shows that in two dimensions it drifts to the right linearly in time.
In this paper, we study the problem of finding the probability that the two-dimensional (biased) monotonic random walk crosses the line $y=\alpha x+d$, where $\alpha,d \geq 0$. A $\beta$-biased monotonic random walk moves from $(a,b)$ to…
We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node. We show that a critical bias strength b_c exists such that most walks find the target within a finite time when b>b_c. For b<b_c,…
It is well known that random walks in one dimensional random environment can exhibit subdiffusive behavior due to presence of traps. In this paper we show that the passage times of different traps are asymptotically independent exponential…
The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…
The Poisson boundary of a finite direct product of affine automorphism groups of homogeneous trees is considered. The Poisson boundary is shown to be a product of ends of trees with a hitting measure for spread-out, aperiodic measures of…
Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian…
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…
{A defining characteristic of Newton's method is local superlinear convergence within a neighbourhood of a strict local minimum. However, outside this neighborhood Newton's method can converge slowly or even diverge. A common approach to…
We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…