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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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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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Redig, F.H.J. (author), van Wiechen, H. (author)
We consider a class of multi-layer interacting particle systems and characterize the set of ergodic probability measures with finite moments. The main technical tool is duality combined with successful coupling.
journal article 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 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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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 self-dualities. In<br/>the...
doctoral thesis 2021
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Carinci, Gioia (author), Giardinà, Cristian (author), Redig, F.H.J. (author)
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the Kipnis-Marchioro-Presutti model. Consistent systems are such that the distribution obtained by first evolving n particles and then removing a particle at random is the same as the one...
journal article 2021
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Carinci, G. (author), Franceschini, Chiara (author), Groenevelt, W.G.M. (author)
We study a class of interacting particle systems with asymmetric interaction showing a self-duality property. The class includes the ASEP(q, θ), asymmetric exclusion process, with a repulsive interaction, allowing up to θ ∈ N particles in each site, and the ASIP(q, θ), θ ∈ R<sup>+</sup>, asymmetric inclusion process, that is its attractive...
journal article 2021
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Angeli, Letizia (author), Grosskinsky, S.W. (author), Johansen, Adam M. (author)
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical ‘cloning’ algorithms have been developed to estimate the scaled cumulant generating function, based on importance sampling...
journal article 2021
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Carinci, G. (author), Giardina', C. (author), Redig, F.H.J. (author)
We consider two particles performing continuous-time nearest neighbor random walk on Z and interacting with each other when they are at neighboring positions. The interaction is either repulsive (partial exclusion process) or attractive (inclusion process). We provide an exact formula for the Laplace-Fourier transform of the transition...
journal article 2020
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Collet, F. (author), Kraaij, R.C. (author)
We modify the spin-flip dynamics of the Curie–Weiss model with dissipation in Dai Pra, Fischer and Regoli (2013) by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for macroscopic observables. We obtain path-space moderate deviation principles via a general analytic...
journal article 2020
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Collet, F. (author), Gorny, Matthias (author), Kraaij, R.C. (author)
The dynamical Curie-Weiss model of self-organized criticality (SOC) was introduced in (Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 658-678) and it is derived from the classical generalized Curie-Weiss by imposing a microscopic Markovian evolution having the distribution of the Curie-Weiss model of SOC (Ann. Probab. 44 (2016) 444-478) as...
journal article 2020
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Sau, 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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Wiarda, Sjoerd (author)
In this thesis we study a class of interacting particle systems sharing a duality property. This class includes the Symmetric Inclusion Process (SIP(2k)), the Symmetric Exclusion Process (SEP(2j)) and the Independent Random Walkers (IRW). When these systems are in equilibrium (namely they are isolated from the exterior) they admit stationary...
bachelor thesis 2019
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Groenevelt, W.G.M. (author), Giardina', C. (author), Redig, F.H.J. (author), Carinci, G. (author)
We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary symmetries of the Markov generator. For these symmetries we provide two equivalent expressions that are related...
journal article 2019
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Collet, F. (author), Kraaij, R.C. (author)
We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie-Weiss model (i.e., standard Curie-Weiss model embedded in a site-dependent, i.i.d. random environment). We obtain path-space moderate deviation principles via a general analytic approach based on convergence of nonlinear generators and...
journal article 2018
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Redig, F.H.J. (author), Sau, F. (author)
We find all self-duality functions of the form (Formula presented.)for a class of interacting particle systems. We call these duality functions of simple factorized form. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion processes, as well as...
journal article 2018
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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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