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van Ginkel, G.J. (author)In this thesis we study the Symmetric Exclusion Process (SEP) and the Discrete Gaussian Free Field (DGFF) on compact Riemannian manifolds. In particular, we obtain the hydrodynamic limit and the equilibrium fluctuations of SEP and we show that the DGFF converges to its continuous counterpart. To define these discrete models, we construct grids...doctoral 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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Corstanje, Marc (author)When data in higher dimensions with a certain constraint on it, say a set of locations on a sphere, is encountered, some classical statistical analysis methods fail, as the data no longer assumes its values in a linear space. In this thesis we consider such datasets and aim to do likelihoodbased inference on the center of the data. To model the...master thesis 2019
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van Ginkel, G.J. (author), Redig, F.H.J. (author)We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider the empirical density field of the symmetric exclusion process and prove that it converges to the...journal article 2019
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Amenta, Alex (author), Tolomeo, Leonardo (author)Given a sequence of complete Riemannian manifolds (Mn) of the same dimension, we construct a complete Riemannian manifold M such that for all p ∈(1,∞) the Lpnorm of the Riesz transform on M dominates the Lpnorm of the Riesz transform on Mn for all n. Thus we establish the following dichotomy: Given p and d, either there is a uniform Lp bound...journal article 2019
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van Ginkel, Bart (author)In this report we study Markov processes on compact and connected Riemannian manifolds. We define a random walk on such manifolds and give a direct proof of the invariance principle. This principle says that under some conditions on the jumping distributions (i.e. the distributions of single steps), the random walk converges to Brownian motion...master thesis 2017
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Versendaal, R. (author)We study the Riesz transform and HodgeDirac operator on a complete Riemannian manifold with Ricci curvature bounded from below. We define the HodgeDirac operator ∏ on Lp(ΛTM) as the closure of d + d* on smooth, compactly supported kforms for 1 < p < ∞. Given the boundedness of the Riesz transform on Lp(ΛTM), we show that ∏ is Rbisectorial on...master thesis 2016