Related papers: Maximal dispersion of adaptive random walks
The deployment of Autonomous Vehicles (AVs) poses considerable challenges and unique opportunities for the design and management of future urban road infrastructure. In light of this disruptive transformation, the Right-Of-Way (ROW)…
This thesis explores a central question: how does memory affect the way random walkers explore space? By analyzing various non-Markovian models, where past behavior directly influences future dynamics, we uncover new mechanisms and…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
Random walks are a common model for exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are…
We analyse the mixing profile of a random walk on a dynamic random permutation, focusing on the regime where the walk evolves much faster than the permutation. Two types of dynamics generated by random transpositions are considered: one…
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…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We consider the activated random walk (ARW) model where particles follow the path of a general Markov process on a general graph. We prove ARW dominates a simpler process, multiple source internal aggregation (MSIA), and use this to…
Random walk is one of the basic mechanisms found in many network applications. We study the epidemic spreading dynamics driven by biased random walks on complex networks. In our epidemic model, each time infected nodes constantly spread…
In this thesis, we study the diffusive and ballistic behaviors of random walk in random environment (RWRE) in an integer lattice with dimension at least 2. Our contributions are in three directions: a conditional law of large numbers and…
We study the dynamics of a radioactive species flowing through a porous material, within the Continuous-Time Random Walk (CTRW) approach to the modelling of stochastic transport processes. Emphasis is given to the case where radioactive…
Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical…
In many open environment applications, data are collected in the form of a stream, which exhibits an evolving distribution over time. How to design algorithms to track these evolving data distributions with provable guarantees, particularly…
Quantum walks (QWs) exhibit different properties compared with classical random walks (RWs), most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as…
Robotic systems must be able to quickly and robustly make decisions when operating in uncertain and dynamic environments. While Reinforcement Learning (RL) can be used to compute optimal policies with little prior knowledge about the…
Many online social networks feature restrictive web interfaces which only allow the query of a user's local neighborhood through the interface. To enable analytics over such an online social network through its restrictive web interface,…
Flow and multicomponent reactive transport in saturated/unsaturated porous media are modeled by ensembles of computational particles moving on regular lattices according to specific random walk rules. The occupation number of the lattice…
A multifractal random walk (MRW) is defined by a Brownian motion subordinated by a class of continuous multifractal random measures $M[0,t], 0\le t\le1$. In this paper we obtain an extension of this process, referred to as multifractal…
Interactive programming environments are powerful tools for promoting innovative network thinking, teaching science of complexity, and exploring emergent phenomena. This paper reports on our recent development of the deterministic random…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…