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Delibas, Murat (author)Various problems related to Random Walk in Random Environments have been researched intensively over the past 40 years by both the mathematics and physics communities. The setup of these problems is quite simple: one defines a Random Walk of choice and allows it to traverse a Random Environment that influences the Random Walk in a predetermined...master thesis 2024
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van Roessel, Milan (author)In this thesis, wealth distribution in a closed economic system is examined by studying the simple inclusion process (SIP). The simple inclusion process is a model coming from statistical physics that models the jumping of particles in a graph. In the model particles have attraction among each other and each site also has a characteristic...bachelor thesis 2023
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van Tol, Berend (author)In this thesis, we study stochastic duality under hydrodynamic scaling in the context of interacting particles on a grid. The approach is inspired and motivated by the relation between duality and local equilibria. We identify duality relations in terms of the expectation of the density field for which the hydrodynamic limit is recovered. This...master thesis 2023
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Benjert, Zylan (author)We consider the problem of random walks moving around on a lattice Zd with an initial Poisson distribution of traps. We consider both static and moving traps. In the static case, we prove that the survival time has a decay of e−c t d /d +2 based on a heuristic argument. In the moving case we aim to prove the sub-exponential...bachelor thesis 2023
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Fokker, Floris (author)In this thesis, the hydrodynamic limit (HDL) for two trapping models is studied, the Random Waiting Time Model (RWTM) and the fractional kinetics process (FKP), on a discrete lattice Zd . The RWTM is studied for dimension d ≥ 1 and E[wi ],∞where wi denotes the waiting time at position i . On the other hand, the FKP is studied for d ≥ 3 and a...bachelor thesis 2023
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Maassen van den Brink, Mitchell (author)In this thesis, research was done in the area of interacting particle systems. Especially, the symmetric exclusion process with local perturbations was investigated. These perturbations, were in the form of sinks and sources, which add or take away particles at certain rates. Moreover, simulations were done for the asymmetric exclusion process....bachelor thesis 2023
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van Kempen, Matt (author)In this paper we started by explaining what a Markov chain is. After this we defined some key concepts such as stationarity, reversibility and ergodicity which were used throughout the rest of the paper. Next, the classical central limit theorem was stated in order to refresh the reader of this theorem and to show that, because of the dependence...bachelor thesis 2022
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Koot, Kees (author)In this thesis the behaviour of a Bose Einstein condensate is explored that consists of bosons that annihilate. In order to do this a system where bose einstein condensation occurs is modeled as a Zero Range process which is a special case of a Markov process.<br/>First we made a single slow site Zero range process with uniform rates and see how...bachelor thesis 2022
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Rissalah, Abdellah (author)In this thesis we study an interacting particle system: the Symmetric Inclusion Process with slowly varying inhomogeneities (SIP(α)). In the SIP(α) particles display random walk like behaviour subjected to an attractive type of interaction whilst evolving in an inhomogeneous environment. We set out to prove its hydrodynamic limit. The main tool...master thesis 2022
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Zegers, Samuel (author)In several experiments, enzymes have shown an in increase in diffusivity in the presence of their substrate. The enhancement in diffusivity ranged from as low as 28% for urease to 80% in the case of alkaline phosphatase. There are two main competing theories. One asserts that catalytically driven boosts propel the enzyme forward in ‘leaps’,...bachelor thesis 2022
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van Tol, Berend (author)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...bachelor thesis 2021
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van Wiechen, Hidde (author)In this thesis we will study the ergodic measures and the hydrodynamic limit of independent run-and-tumble particle processes, i.e., an interacting particle system for particles with an internal energy source, which makes them move in a preferred direction that changes at random times. We start by providing some basic concepts and theory of...master thesis 2021
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Meskers, Marthe (author)In this thesis, we study the asymptotic behaviour and the dynamics of a one-dimensional active particle model with excluded volume interactions. The model is a version of run-and-tumble motion, where a particle performs both symmetric random walks and active transport. The direction and the speed of the transport are governed by an internal...bachelor thesis 2021
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Holtrop, Sven (author)In this thesis, the diffusive limit of active particle motion in R<sup>d</sup> is studied via a technique based on homogenisation. Thereafter, this study is extended to active particle motion on a Riemannian manifold. <br/><br/>Furthermore, as an application of active particle motion, a connection is made with the Dirac equation. On the basis of...bachelor thesis 2021
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Zaat, Justin (author)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...bachelor thesis 2019
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Hoogendijk, Jochem (author)This project aims to describe crude models that work towards a mathematical model for transcription and translation. Transcription refers to the conversion of genetic code to a readable format for the cell, while translation refers to the conversion of this code into polypeptide chains using ribosomes. The main proposal for such a model is the...bachelor thesis 2019
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Leenders, Mats (author)In this paper a two agent wealth distribution model for a closed economic system developed in [2] is presented and extended. We first extend the model by randomly distributing the propensity to save of the agents. We derive a closed form of the stationary relative wealth measure of an agent. We also see that if we take both the propensity to...bachelor thesis 2019
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Westdorp, Rik (author)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...bachelor thesis 2018
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Ayala-Valenzuela, M.A. (author)This thesis deals with the proof of the hydrodynamic limit for the symmetric inclusion process (SIP). After introduction of our process and some basic concepts on the theory of Markov processes we proved self-duality for the SIP. Once equipped with SIP self-duality, and together with an assumption on the initial configuration, we were able to...master thesis 2016
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Jongbloed, H. (author)The Abelian Sandpile model was originally introduced by Bak, Tang and Wiesenfeld in 1987 as a paradigm for self-organized criticality. In this thesis, we study a variant of this model, both from the point of view of mathematics, as well as from the point of view of physics. The effect of dissipation and creation of mass is investigated. By...bachelor thesis 2016
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