Related papers: First-passage times to quantify and compare struct…
The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
In a spatial-temporal model, structural change and/or spatial heterogeneity can easily affect estimation of parameters. Following the spatial-temporal model in [1], we develop a nonparametric procedure for test-ing the presence of…
First-passage time problems are ubiquitous across many fields of study including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage time…
A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended…
Current is a characteristic feature of nonequilibrium systems. In stochastic systems, these currents exhibit fluctuations constrained by the rate of dissipation in accordance with the recently discovered thermodynamic uncertainty relation.…
Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Often sharp changes in cellular behavior are triggered by thresholded events, i.e., by the attainment of a threshold value of a relevant cellular or molecular dynamical variable. Since the governing variable itself typically undergoes noisy…
Various graph algorithms have been developed with multiple random walks, the movement of several independent random walkers on a graph. Designing an efficient graph algorithm based on multiple random walks requires investigating multiple…
We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination…
We present a unified framework for first-passage time and residence time of random walks in finite one-dimensional disordered biased systems. The derivation is based on exact expansion of the backward master equation in cumulants. The…
In a system of many similar self-propelled entities such as flocks of birds, fish school, cells and molecules, the interactions with neighbors can lead to a "coherent state", meaning the formation of visually compelling aggregation patterns…
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…