Related papers: Synchronization of random walks with reflecting bo…
We consider two dimensional random walks conditioned to stay in the positive quadrant. Assuming that the increments of the walk have finite second moments and that the drift vector is co-oriented with one of two axes, we construct positive…
We employ a quantum trajectory approach to characterize synchronization and phase-locking between open quantum systems in nonequilibrium steady states. We exemplify our proposal for the paradigmatic case of two quantum Van der Pol…
In scalable machine learning systems, model training is often parallelized over multiple nodes that run without tight synchronization. Most analysis results for the related asynchronous algorithms use an upper bound on the information…
In this paper we study the number of returns to the coordinate hyperplanes for multidimensional nearest-neighbour random walks. While one-dimensional results on returns are classical, much less is known in higher dimensions. We analyse the…
In this paper we study the synchronization properties of random geometric graphs. We show that the onset of synchronization takes place roughly at the same value of the order parameter that a random graph with the same size and average…
We consider a random walk on the first quadrant of the square lattice, whose increment law is, roughly speaking, homogeneous along a finite number of half-lines near each of the two boundaries, and hence essentially specified by…
In previous work by Avena and den Hollander, a model of a one-dimensional random walk in a dynamic random environment was proposed where the random environment is resampled from a given law along a growing sequence of deterministic times.…
We consider a generalization of the so-called elephant random walk by introducing multiple elephants moving along the integer line, $\mathbb{Z}$. When taking a new step, each elephant considers not only its own previous steps but also the…
Colloidal bodies of irregular shape rotate as they descend under gravity in solution. This rotational response provides a means of bringing a dispersion of identical bodies into a synchronized rotation with the same orientation using…
We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to…
Synchronized behavior among individuals is a ubiquitous feature of populations. Understanding mechanisms of (de)synchronization demands meaningful, interpretable, computable quantifications of synchrony, relevant to measurements that can be…
Experimental realization and quantitative investigation of common-noise-induced synchronization of limit-cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit. Based on our previous…
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…
A random walk in random scenery $(Y_n)_{n\in\mathbb{N}}$ is given by $Y_n=\xi_{S_n}$ for a random walk $(S_n)_{n\in\mathbb{N}}$ and iid random variables $(\xi_n)_{n\in\mathbb{Z}}$. In this paper, we will show the weak convergence of the…
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…
We focus on two models of nearest-neighbour random walks on d-dimensional regular hyper-cubic lattices that are usually assumed to be identical - the discrete-time Polya walk, in which the walker steps at each integer moment of time, and…
We study the relaxation time in the random walk with jumps. The random walk with jumps combines random walk based sampling with uniform node sampling and improves the performance of network analysis and learning tasks. We derive various…
We quantify the dynamical implications of the small-world phenomenon. We consider the generic synchronization of oscillator networks of arbitrary topology, and link the linear stability of the synchronous state to an algebraic condition of…
A random walk generated by a sum of independent identity distributed random variables with positive expectation is considered. The limiting distributions for the first- passage -time of a step-function boundary are derived.
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…