The effect of measurement uncertainties on quantum random walk based problems

Random walks have been used in a number of different fields for a long time. With the rise of of quantum random walks a lot of these applications have been made more efficient. Recently there have been a lot of improvements in the realization of these quantum random walks in real world systems. <br/>In this research, the effect of uncertainty in...

Criticality in the Abelian sandpile model

In this thesis we study criticality in the context of the dissipative Abelian sandpile model. The model is linked to a simple trapped random walk, giving a practical method to determine criticality for certain landscapes of dissipative sites. The main results concern the lifetime of the random walk, especially the divergence of its first moment...

Improving the Anonymity of Blockchains: The Case of Payment Channel Networks with Length-bounded Random Walk Insertion

The LND is currently the most popular routing algorithm used in the Lightning Network, the second layer solution to Bitcoin’s scalability. Despite its popularity, recent studies demonstrate that its deterministic nature compromises the anonymity of the Lightning Network. In other words, threatening parties present in the transaction path can...

The electric network approach to the study of Markov Chains

Markov chains are used to describe random processes in discrete time, which have the property of being memoryless. This report covers Markov chains on a finite space that are homogeneous in time and mainly follows the structure of ''Markov Chains and Mixing Times''. Markov chains exhibit a strong connection with electric networks. We exploit...

Dissipation in the Abelian sandpile model: Conditions for criticality

The Abelian sandpile model was first introduced by Bak, Tang and Wiesenfeld in 1987. Since then, a lot of researchers have studied this model and similar models, all related by the concept of self-organized criticality. In this thesis, we study a variant on the classical model where dissipative and anti-dissipative vertices are incorporated in...

Scaling limits of long-range quantum random walks

In this thesis we introduce a variation on the quantum random walk to discuss shifts in an arbitrary range. The concept of Hadamard coin was therefore generalised to a higher order. By a Fourier transform method and a tensor product decomposition of the evolution matrix the long-range quantum random walk was found to converge in distribution to...

Particle models for sand transport in water: analysis and simulations

This thesis describes how the simple random walk particle model can be extended to account for sand deposition and suspension, and for particle interaction: clumping together and falling apart. The extended models are analyzed, and the corresponding partial differential equations are derived. These equations are compared to the currently used...

Using an Agent-Based Formalism to Simulate Passenger Flows

In this report two Agent-Based Models, the Passenger Model and the Transfer Model, will be constructed and analyzed. The objective is to make a realistic model inspired by a cell-based model to simulate passenger flows on a train platform. We will start by studying the cell-based model and we will explain which aspects have been applied to our...