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Diffusion et relaxation pour des systèmes de particules avec contraintes cinétiques

Abstract : This PhD thesis focuses on Kinetically Constrained Models, also known as KCM. These models are continuous time Markov process on the state space {0,1}^G, where G is the set of vertices of a graph, usually Z^d. KCMs were introduced in the 1980's by physicists in order to model liquid/glass transition. The work presented here is split in two main results. First, we study a particular spin model called the Fredrickson-Andersen model, for which we establish a precise relaxation result. More precisely, we show that this process exhibits cutoff by giving an estimate on the mixing time starting from any initial configuration. Next, we focus on another model that is conservatif, for which we follow the motion of a tagged particle. It was recently show that the trajectory of the particle is diffusive, and that the diffusion coefficient is positive. Here, we push this result further by giving precise bounds on this coefficient when the particle density tends to 1.
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Submitted on : Wednesday, June 22, 2022 - 12:25:23 PM
Last modification on : Thursday, June 23, 2022 - 3:37:19 AM


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  • HAL Id : tel-03701634, version 1


Anatole Ertul. Diffusion et relaxation pour des systèmes de particules avec contraintes cinétiques. Physique mathématique [math-ph]. Université de Lyon, 2021. Français. ⟨NNT : 2021LYSE1270⟩. ⟨tel-03701634⟩



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