Related papers: Clusters determine local fluctuations of random wa…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
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…
We consider a class of graph-valued stochastic processes in which each vertex has a type that fluctuates randomly over time. Collectively, the paths of the vertex types up to a given time determine the probabilities that the edges are…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
In 2008, T\'oth and Vet\H{o} defined the self-repelling random walk with directed edges as a non-Markovian random walk on $\mathbb{Z}$: in this model, the probability that the walk moves from a point of $\mathbb{Z}$ to a given neighbor…
We investigate the statistics of fluctuations in a classical stochastic network of nodes joined by connectors. The nodes carry generalized charge that may be randomly transferred from one node to another. Our goal is to find the time…
A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is…
The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…
Conditions on the generator of a Markov process to control the fluctuations of its bridges are found. In particular, continuous time random walks on graphs and gradient diffusions are considered. Under these conditions, a concentration of…
Nodes can be ranked according to their relative importance within the network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based…
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…
Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…
Given an underlying graph, we consider the following \emph{dynamics}: Initially, each node locally chooses a value in $\{-1,1\}$, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its…
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…
Analyzing the mixing time of random walks is a well-studied problem with applications in random sampling and more recently in graph partitioning. In this work, we present new analysis of random walks and evolving sets using more…
We suggest a model for data losses in a single node of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. The model shows critical behavior with an abrupt…
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…
Several stochastic processes modeling molecular motors on a linear track are given by random walks (not necessarily Markovian) on quasi 1d lattices and share a common regenerative structure. Analyzing this abstract common structure, we…
Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity $\vec{v}$, the common mean velocity of the random…
Financial price changes obey two universal properties: they follow a power law and they tend to be clustered in time. The second regularity, known as volatility clustering, entails some predictability in the price changes: while their sign…