Related papers: All-time dynamics of continuous-time random walks …
A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study…
We study the dynamics of continuous-time quantum walks (CTQW) on networks with highly degenerate eigenvalue spectra of the corresponding connectivity matrices. In particular, we consider the two cases of a star graph and of a complete…
Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
Annual maximum temperature data provides crucial insights into the impacts of climate change, especially for regions like India, where temperature variations have significant implications for agriculture, health, and infrastructure. In this…
We introduce a discrete-time quantum random walk (QRW) framework for spatial epidemic modelling on a two-dimensional square lattice and compare its dynamics to classical random-walk SIR models. In our model, each infected site spawns a…
We study the classical and quantum transport processes on some finite networks and model them by continuous-time random walks (CTRW) and continuous-time quantum walks (CTQW), respectively. We calculate the classical and quantum transition…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…
Starting from a continuous time random walk (CTRW) model of particles that may evanesce as they walk, our goal is to arrive at macroscopic integro-differential equations for the probability density for a particle to be found at point r at…
Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of…
A detailed study is presented for a large class of uncoupled continuous-time random walks (CTRWs). The master equation is solved for the Mittag-Leffler survival probability. The properly scaled diffusive limit of the master equation is…
We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the "environment seen from the walker"-process and in particular its…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.
Temporal networks, i.e., networks in which the interactions among a set of elementary units change over time, can be modelled in terms of time-varying graphs, which are time-ordered sequences of graphs over a set of nodes. In such graphs,…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
In recent years a huge interdisciplinary field has emerged which is devoted to the complex dynamics of anomalous transport with long-time memory and non-markovian features. It was found that the framework of fractional calculus and its…