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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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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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Floreani, S. (author)Interacting particle systems (IPS) is a subfield of probability theory that provided a fruitful framework in which several questions of physical interests have been answered with mathematical rigor. An interacting particle system is a stochastic system consisting of a very large number of particles interacting with each other. The class of IPS...doctoral 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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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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van Wiechen, Hidde (author)In this thesis we will study the ergodic measures and the hydrodynamic limit of independent runandtumble 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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Floreani, S. (author), Redig, F.H.J. (author), Sau, Federico (author)In this paper, we introduce a random environment for the exclusion process in Z<sup>d</sup> obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we...journal article 2021
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Redig, F.H.J. (author), Saada, Ellen (author), Sau, Federico (author)We consider the symmetric simple exclusion process in Z<sup>d</sup> with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the selfduality of the process, between the invariance principle for single particles starting from all points and the macroscopic...journal article 2020
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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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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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AyalaValenzuela, 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 selfduality for the SIP. Once equipped with SIP selfduality, and together with an assumption on the initial configuration, we were able to...master thesis 2016