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We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…
Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed…
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance…
Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from…
Random walk is one of the most classical and well-studied model in probability theory. For two correlated random walks on lattice, every step of the random walks has only two states, moving in the same direction or moving in the opposite…
The theory of rapid mixing random walks plays a fundamental role in the study of modern randomised algorithms. Usually, the mixing time is measured with respect to the worst initial position. It is well known that the presence of…
We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified…
We study the synchronized interval in undirected and unweighted random networks of coupled oscillators as a function of the number of edges. In many coupled oscillator systems, synchronization is stable in a finite interval of coupling…
The waiting time needed for a stock market index to undergo a given percentage change in its value is found to have an up-down asymmetry, which, surprisingly, is not observed for the individual stocks composing that index. To explain this,…
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…
For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the…
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the…
This paper explores the mixing time of the random transposition walk on the symmetric group. While it has long been known that this walk mixes in order n*log(n) time, this result has not previously been attained using coupling. A coupling…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov…
Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior while others behave erratically. Predicting the emergence of these clusters and understanding the…