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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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Cheng, D. (author)This dissertation collects three scientific contributions, already published in international peerreviewed journals, plus some extra considerations and workinprogress. First, we present a model based on reinforced urn processes, which conjugates to the rightcensored recovery process, and empirically apply it to the time series of recovery...doctoral 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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Ayala Valenzuela, M.A. (author)This thesis is concerned with fluctuations of interacting particle systems that<br/>enjoy the property of duality. The main contributions of this work are divided<br/>in two main parts. In the first part we study some of the advantages of looking<br/>at the density fluctuation field through the lenses of orthogonal selfdualities. In<br/>the...doctoral thesis 2021
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Versendaal, R. (author)This thesis is concerned with large deviations for processes in Riemannian manifolds. In particular, we study the extensions of large deviations for random walks and Brownian motion to the geometric setting. Furthermore, we also consider large deviations for random walks in Lie groups. The additional group structure allows for improvements over...doctoral thesis 2020
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de Jonge, C.J. (author)In this thesis continued fractions are studied in three directions: semiregular continued fractions, Nakada’s αexpansions and Nexpansions. In Chapter 1 the general concept of a continued fraction is given, involving an operator that yields the partial quotients or digits of a continued fraction expansion. The approximation coefficients θ_n(x)...doctoral thesis 2020
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Symmetric interacting particle systems: Selfduality and hydrodynamics in dynamic random environmentSau, F. (author)In this thesis, we study scaling and detailed properties of a class of conservative interacting particle systems. In particular, in the first part we derive the hydrodynamic equation for the symmetric exclusion process in presence of dynamic random environment. The second part of the thesis focuses on a detailed property of conservative particle...doctoral thesis 2019
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 Kraaij, R.C. (author) doctoral thesis 2016
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Völlering, F.M. (author)In this thesis we discuss concentration inequalities, relaxation to equilibrium of stochastic dynamics, and random walks in dynamic random environments. In stochastic systems one is interested in macroscopic and/or asymptotic properties as well as in fluctuations around typical behaviour. But the dependence structure induced by the interaction...doctoral thesis 2012