Related papers: Record statistics for a discrete-time random walk …
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
In this paper analogies between different (dis)similarity matrices are derived. These matrices, which are connected to path enumeration and random walks, are used in community detection methods or in computation of centrality measures for…
This paper is concerned with the limit theory of the extreme order statistics derived from random walks. We establish the joint convergence of the order statistics near the minimum of a random walk in terms of the Feller chains. Detailed…
In these lecture notes I will discuss the universal first-passage properties of a simple correlated discrete-time sequence {x_0=0, x_1,x_2.... x_n} up to n steps where x_i represents the position at step i of a random walker hopping on a…
Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$.…
We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
Random walk subject to random drive has been extensively employed as a model for physical and biological processes. While equilibrium statistical physics has yielded significant insights into the distributions of dynamical fixed points of…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
The evolution of many dynamical systems that describe relationships or interactions between objects can be effectively modeled by temporal networks, which are typically represented as a sequence of static network snapshots. In this paper,…
Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous…
The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that…
We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [-a,a]. For a of the order of one, the exit probabilities to each edge of the…
We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…
This paper concerns the long-term behaviour of a system of interacting random walks labeled by vertices of a finite graph. The model is reversible which allows to use the method of electric networks in the study. In addition, examples of…
We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
Time series data that are not measured at regular intervals are commonly discretized as a preprocessing step. For example, data about customer arrival times might be simplified by summing the number of arrivals within hourly intervals,…
For any physical observable in statistical systems, the most frequently studied quantities are its average and standard deviation. Yet, its full distribution often carries extremely interesting information and can be invoked to put any…
The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…