Related papers: Maximal dispersion of adaptive random walks
In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…
Algebraic random walks (ARW) and quantum mechanical random walks (QRW) are investigated and related. Based on minimal data provided by the underlying bialgebras of functions defined on e. g the real line R, the abelian finite group Z_N, and…
Excited random walks (ERWs) are a self-interacting non-Markovian random walk in which the future behavior of the walk is influenced by the number of times the walk has previously visited its current site. We study the speed of the walk,…
We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous…
Random walks on dynamic graphs have received increasingly more attention from different academic communities over the last decade. Despite the relatively large literature, little is known about random walks that construct the graph where…
In this article we shall derive functional limit theorems for the multi-dimensional elephant random walk (MERW) and thus extend the results provided for the one-dimensional marginal by Bercu and Laulin (2019). The MERW is a non-Markovian…
We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate…
Activated Random Walk (ARW) is an interacting particle system on the $d$-dimensional lattice $\mathbb{Z}^d$. On a finite subset $V \subset \mathbb{Z}^d$ it defines a Markov chain on $\{0,1\}^V$. We prove that when $V$ is a Euclidean ball…
Message-passing architectures struggle to sufficiently model long-range dependencies in node and graph prediction tasks. We propose a novel approach exploiting hierarchical graph structures and adaptive random walks to address this…
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been…
Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal…
Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently in the presence of some obstacles or constraints. A somewhat related class of problems focuses…
How to enable efficient analytics over such data has been an increasingly important research problem. Given the sheer size of such social networks, many existing studies resort to sampling techniques that draw random nodes from an online…
The choice of the increment distribution is crucial for the random-walk Metropolis-Hastings (RWM) algorithm. In this paper we study the optimal choice in high-dimension setting among all possible increment distributions. The conclusion is…
The Activated Random Walk (ARW) model is a promising candidate for demonstrating self-organized criticality due to its potential for universality. Recent studies have shown that the ARW model exhibits a well-defined critical density in one…
Network embedding aims to represent a network into a low dimensional space where the network structural information and inherent properties are maximumly preserved. Random walk based network embedding methods such as DeepWalk and node2vec…
The technique of detecting multiple dim and small targets with low signal-to-clutter ratios (SCR) is very important for infrared search and tracking systems. In this paper, we establish a detection method derived from maximal entropy random…
Discriminative Random Walks (DRWs) are a simple yet powerful tool for semi-supervised node classification, but their theoretical foundations remain fragmentary. We revisit DRWs through the lens of information geometry, treating the family…