Related papers: Synchronization of random walks with reflecting bo…
We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…
A random walk with echoed steps (RWES) is a process $\{\tilde{S}_n\}_{n\geq1}=\{\tilde{X}_1+\cdots+\tilde{X}_n\}_{n\geq1}$ that inserts memory and echo into an ordinary random walk (ORW) with i.i.d. steps, $X_1+\cdots+X_n$. The RWES is…
We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in…
In this paper, we study the scaling limit of a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. If the probability of…
For linear networks, where the coupling between the agents takes place through periodic impulses, a simple method is proposed for synchronization. It is shown that closing the loop by (normalized) deadbeat feedback gain produces synchronous…
The dynamics of three mutually coupled cortical neurons with time delays in the coupling are explored numerically and analytically. The neurons are coupled in a line, with the middle neuron sending a somewhat stronger projection to the…
We derive a local limit theorem for normal, moderate, and large deviations for symmetric simple random walk on the square lattice in dimensions one and two that is an improvement of existing results for points that are particularly distant…
The problem of time synchronization in dense wireless networks is considered. Well established synchronization techniques suffer from an inherent scalability problem in that synchronization errors grow with an increasing number of hops…
In this article, we first give a comprehensive description of random walk (RW) problem focusing on self-similarity, dynamic scaling and its connection to diffusion phenomena. One of the main goals of our work is to check how robust the RW…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…
We outline basic properties of a symmetric random walk in one dimension, in which the length of the nth step equals lambda^n, with lambda<1. As the number of steps N-->oo, the probability that the endpoint is at x, P_{lambda}(x;N),…
We propose a model of a one-dimensional random walk in dynamic random environment that interpolates between two classical settings: (I) the random environment is sampled at time zero only; (II) the random environment is resampled at every…
Algorithms for the synchronisation of clocks across networks are both common and important within distributed systems. We here address not only the formal modelling of these algorithms, but also the formal verification of their behaviour.…
A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This result unifies and extends previous work on repeated-interactions models, including that of the author (2010, J. London Math. Soc.…
We introduce and study systems of randomly coupled maps (RCM) where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally…
In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
In this paper, we study random walks evolving with a directional bias in a two-dimensional random environment with correlations that vanish polynomially. Using renormalization methods first employed for one-dimensional dynamic environments…