Related papers: Variable-step-length algorithms for a random walk:…
Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…
We consider homogeneous random walks in the quarter-plane. The necessary conditions which characterize random walks of which the invariant measure is a sum of geometric terms are provided in [2,3]. Based on these results, we first develop…
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…
Traditional force-controlled bipedal walking utilizes highly bent knees, resulting in high torques as well as inefficient, and unnatural motions. Even with advanced planning of center of mass height trajectories, significant amounts of…
We generalize the Metropolis et al. random walk algorithm to the situation where the energy is noisy and can only be estimated. Two possible applications are for long range potentials and for mixed quantum-classical simulations. If the…
We study in-network computation on general network topologies. Specifically, we are given the description of a function, and a network with distinct nodes at which the operands of the function are made available, and a designated sink where…
We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the…
In recent years there has been substantial development in algorithms for quantum phase estimation. In this work we provide a new approach to online Bayesian phase estimation that achieves Heisenberg limited scaling that requires…
The iterated random walk is a random process in which a random walker moves on a one-dimensional random walk which is itself taking place on a one-dimensional random walk, and so on. This process is investigated in the continuum limit using…
Predicting links in complex networks has been one of the essential topics within the realm of data mining and science discovery over the past few years. This problem remains an attempt to identify future, deleted, and redundant links using…
Random walks are a fundamental primitive used in many machine learning algorithms with several applications in clustering and semi-supervised learning. Despite their relevance, the first efficient parallel algorithm to compute random walks…
In this note, we compute the probability that a two-dimensional symmetric random walk visits more vertices than expected, for deviations on scales between the mean behavior and linear growth.
The cost of stochastic resetting is considered within the context of a discrete random walk model. In addition to standard stochastic resetting, for which a reset occurs with a certain probability after \emph{each} step, we introduce a…
We consider a one dimensional ballistic random walk evolving in an i.i.d. parametric random environment. We provide a maximum likelihood estimation procedure of the environment parameters based on a single observation of the path till the…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…
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 perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on…
Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…